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Diketahui A=(1−1​2−1​), B=(10​1−1​), dan C=(0−1​10​). Tentukan: b.    A7+B7−C7

Pertanyaan

Diketahui A equals open parentheses table row 1 2 row cell negative 1 end cell cell negative 1 end cell end table close parenthesesB equals open parentheses table row 1 1 row 0 cell negative 1 end cell end table close parentheses, dan C equals open parentheses table row 0 1 row cell negative 1 end cell 0 end table close parentheses. Tentukan:

b.    begin mathsize 14px style A to the power of 7 plus B to the power of 7 minus C to the power of 7 end style 

Pembahasan Soal:

Oleh karena A to the power of 7 equals A squared times A squared times A squared times A, maka dengan menyubtitusi A equals open parentheses table row 1 2 row cell negative 1 end cell cell negative 1 end cell end table close parentheses ke A squared terlebih dahulu, 

table attributes columnalign right center left columnspacing 0px end attributes row cell A squared end cell equals cell open parentheses table row 1 2 row cell negative 1 end cell cell negative 1 end cell end table close parentheses squared end cell row blank equals cell open parentheses table row 1 2 row cell negative 1 end cell cell negative 1 end cell end table close parentheses open parentheses table row 1 2 row cell negative 1 end cell cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 1 open parentheses 1 close parentheses plus 2 open parentheses negative 1 close parentheses end cell cell 1 open parentheses 2 close parentheses plus 2 open parentheses negative 1 close parentheses end cell row cell negative 1 open parentheses 1 close parentheses plus open parentheses negative 1 close parentheses open parentheses negative 1 close parentheses end cell cell negative 1 open parentheses 2 close parentheses plus open parentheses negative 1 close parentheses open parentheses negative 1 close parentheses end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 1 plus open parentheses negative 2 close parentheses end cell cell 2 plus open parentheses negative 2 close parentheses end cell row cell open parentheses negative 1 close parentheses plus 1 end cell cell open parentheses negative 2 close parentheses plus 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 1 end cell 0 row 0 cell negative 1 end cell end table close parentheses subscript blank subscript text      ingat: end text space k open parentheses table row a b row c d end table close parentheses equals open parentheses table row cell k a end cell cell k b end cell row cell k c end cell cell k d end cell end table close parentheses end subscript end subscript end cell row blank equals cell open parentheses table row cell open parentheses negative 1 close parentheses 1 end cell cell open parentheses negative 1 close parentheses 0 end cell row cell open parentheses negative 1 close parentheses 0 end cell cell open parentheses negative 1 close parentheses 1 end cell end table close parentheses end cell row blank equals cell open parentheses negative 1 close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses end cell end table 

sehingga diperoleh

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell A to the power of 7 end cell equals cell A squared times A squared times A squared times A end cell row blank equals cell open parentheses negative 1 close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses negative 1 close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses negative 1 close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 1 2 row cell negative 1 end cell cell negative 1 end cell end table close parentheses subscript text  ingat:  end text k M equals M k end subscript end cell row blank equals cell open parentheses negative 1 close parentheses open parentheses negative 1 close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses negative 1 close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 1 2 row cell negative 1 end cell cell negative 1 end cell end table close parentheses subscript blank subscript table attributes columnalign left end attributes row cell text ingat: end text end cell row cell open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses equals open parentheses table row 1 0 row 0 1 end table close parentheses end cell end table end subscript end subscript end cell row blank equals cell open parentheses negative 1 close parentheses open parentheses negative 1 close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses negative 1 close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 1 2 row cell negative 1 end cell cell negative 1 end cell end table close parentheses subscript text  ingat:  end text k M equals M k end subscript end cell row blank equals cell open parentheses negative 1 close parentheses open parentheses negative 1 close parentheses open parentheses negative 1 close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 1 2 row cell negative 1 end cell cell negative 1 end cell end table close parentheses subscript text  ingat:  end text open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses equals open parentheses table row 1 0 row 0 1 end table close parentheses end subscript end cell row blank equals cell open parentheses negative 1 close parentheses open parentheses negative 1 close parentheses open parentheses negative 1 close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 1 2 row cell negative 1 end cell cell negative 1 end cell end table close parentheses subscript space text ingat:  end text open parentheses table row 1 0 row 0 1 end table close parentheses M equals M end subscript end cell row blank equals cell open parentheses negative 1 close parentheses open parentheses negative 1 close parentheses open parentheses negative 1 close parentheses open parentheses table row 1 2 row cell negative 1 end cell cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses negative 1 close parentheses open parentheses table row 1 2 row cell negative 1 end cell cell negative 1 end cell end table close parentheses subscript text  ingat:  end text k open parentheses table row a b row c d end table close parentheses equals open parentheses table row cell k a end cell cell k b end cell row cell k c end cell cell k d end cell end table close parentheses end subscript end cell row blank equals cell open parentheses table row cell open parentheses negative 1 close parentheses 1 end cell cell open parentheses negative 1 close parentheses 2 end cell row cell open parentheses negative 1 close parentheses minus 1 end cell cell open parentheses negative 1 close parentheses minus 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 1 end cell cell negative 2 end cell row 1 1 end table close parentheses end cell end table end style

Oleh karena B to the power of 7 equals B squared times B squared times B squared times B, maka dengan menyubtitusi B equals open parentheses table row 1 1 row 0 cell negative 1 end cell end table close parentheses ke B squared terlebih dahulu, 

table attributes columnalign right center left columnspacing 0px end attributes row cell B squared end cell equals cell open parentheses table row 1 1 row 0 cell negative 1 end cell end table close parentheses squared end cell row blank equals cell open parentheses table row 1 1 row 0 cell negative 1 end cell end table close parentheses open parentheses table row 1 1 row 0 cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 1 open parentheses 1 close parentheses plus 1 open parentheses 0 close parentheses end cell cell 1 open parentheses 1 close parentheses plus 1 open parentheses negative 1 close parentheses end cell row cell 0 open parentheses 1 close parentheses plus open parentheses negative 1 close parentheses open parentheses 0 close parentheses end cell cell 0 open parentheses 1 close parentheses plus open parentheses negative 1 close parentheses open parentheses negative 1 close parentheses end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 1 plus 0 end cell cell 1 plus open parentheses negative 1 close parentheses end cell row cell 0 plus 0 end cell cell 0 plus 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row 1 0 row 0 1 end table close parentheses end cell end table 

sehingga diperolah

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell B to the power of 7 end cell equals cell B squared times B squared times B squared times B end cell row blank equals cell open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 1 1 row 0 cell negative 1 end cell end table close parentheses subscript space space text karena  end text open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses equals open parentheses table row 1 0 row 0 1 end table close parentheses end subscript end cell row blank equals cell open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 1 1 row 0 cell negative 1 end cell end table close parentheses subscript space space text karena  end text open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses equals open parentheses table row 1 0 row 0 1 end table close parentheses end subscript end cell row blank equals cell open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 1 1 row 0 cell negative 1 end cell end table close parentheses subscript space space text karena  end text open parentheses table row 1 0 row 0 1 end table close parentheses M equals M end subscript end cell row blank equals cell open parentheses table row 1 1 row 0 cell negative 1 end cell end table close parentheses end cell end table end style

Oleh karena C to the power of 7 equals C squared times C squared times C squared times C, maka dengan menyubtitusi C equals open parentheses table row 0 1 row cell negative 1 end cell 0 end table close parentheses ke C squared terlebih dahulu, 

table attributes columnalign right center left columnspacing 0px end attributes row cell C squared end cell equals cell open parentheses table row 0 1 row cell negative 1 end cell 0 end table close parentheses squared end cell row blank equals cell open parentheses table row 0 1 row cell negative 1 end cell 0 end table close parentheses open parentheses table row 0 1 row cell negative 1 end cell 0 end table close parentheses end cell row blank equals cell open parentheses table row cell 0 open parentheses 0 close parentheses plus 1 open parentheses negative 1 close parentheses end cell cell 0 open parentheses 1 close parentheses plus 1 open parentheses 0 close parentheses end cell row cell open parentheses negative 1 close parentheses open parentheses 0 close parentheses plus 0 open parentheses negative 1 close parentheses end cell cell open parentheses negative 1 close parentheses open parentheses 1 close parentheses plus 0 open parentheses 0 close parentheses end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 0 plus open parentheses negative 1 close parentheses end cell cell 0 plus 0 end cell row cell 0 plus 0 end cell cell open parentheses negative 1 close parentheses plus 0 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 1 end cell 0 row 0 cell negative 1 end cell end table close parentheses subscript text      ingat: end text space k open parentheses table row a b row c d end table close parentheses equals open parentheses table row cell k a end cell cell k b end cell row cell k c end cell cell k d end cell end table close parentheses end subscript end cell row blank equals cell open parentheses table row cell open parentheses negative 1 close parentheses 1 end cell cell open parentheses negative 1 close parentheses 0 end cell row cell open parentheses negative 1 close parentheses 0 end cell cell open parentheses negative 1 close parentheses 1 end cell end table close parentheses end cell row blank equals cell open parentheses negative 1 close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses end cell end table 

sehingga diperoleh

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell C to the power of 7 end cell equals cell C squared times C squared times C squared times C end cell row blank equals cell open parentheses negative 1 close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses negative 1 close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses negative 1 close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 0 1 row cell negative 1 end cell 0 end table close parentheses subscript text  ingat:  end text k M equals M k end subscript end cell row blank equals cell open parentheses negative 1 close parentheses open parentheses negative 1 close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses negative 1 close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 0 1 row cell negative 1 end cell 0 end table close parentheses subscript blank subscript table attributes columnalign left end attributes row cell text ingat: end text end cell row cell open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses equals open parentheses table row 1 0 row 0 1 end table close parentheses end cell end table end subscript end subscript end cell row blank equals cell open parentheses negative 1 close parentheses open parentheses negative 1 close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses negative 1 close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 0 1 row cell negative 1 end cell 0 end table close parentheses subscript text  ingat:  end text k M equals M k end subscript end cell row blank equals cell open parentheses negative 1 close parentheses open parentheses negative 1 close parentheses open parentheses negative 1 close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 0 1 row cell negative 1 end cell 0 end table close parentheses subscript text  ingat:  end text open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses equals open parentheses table row 1 0 row 0 1 end table close parentheses end subscript end cell row blank equals cell open parentheses negative 1 close parentheses open parentheses negative 1 close parentheses open parentheses negative 1 close parentheses open parentheses table row 1 0 row 0 1 end table close parentheses open parentheses table row 0 1 row cell negative 1 end cell 0 end table close parentheses subscript space text ingat:  end text open parentheses table row 1 0 row 0 1 end table close parentheses M equals M end subscript end cell row blank equals cell open parentheses negative 1 close parentheses open parentheses negative 1 close parentheses open parentheses negative 1 close parentheses open parentheses table row 0 1 row cell negative 1 end cell 0 end table close parentheses end cell row blank equals cell open parentheses negative 1 close parentheses open parentheses table row 0 1 row cell negative 1 end cell 0 end table close parentheses subscript text  ingat:  end text k open parentheses table row a b row c d end table close parentheses equals open parentheses table row cell k a end cell cell k b end cell row cell k c end cell cell k d end cell end table close parentheses end subscript end cell row blank equals cell open parentheses table row cell open parentheses negative 1 close parentheses 0 end cell cell open parentheses negative 1 close parentheses 1 end cell row cell open parentheses negative 1 close parentheses minus 1 end cell cell open parentheses negative 1 close parentheses 0 end cell end table close parentheses end cell row blank equals cell open parentheses table row 0 cell negative 1 end cell row 1 0 end table close parentheses end cell end table end style

Dengan demikian, 

table attributes columnalign right center left columnspacing 0px end attributes row cell A to the power of 7 plus B to the power of 7 minus C to the power of 7 end cell equals cell open parentheses table row cell negative 1 end cell cell negative 2 end cell row 1 1 end table close parentheses plus open parentheses table row 1 1 row 0 cell negative 1 end cell end table close parentheses minus open parentheses table row 0 cell negative 1 end cell row 1 0 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 1 plus 1 minus 0 end cell cell negative 2 plus 1 minus open parentheses negative 1 close parentheses end cell row cell 1 plus 0 minus 1 end cell cell 1 plus open parentheses negative 1 close parentheses minus 0 end cell end table close parentheses end cell row blank equals cell open parentheses table row 0 0 row 0 0 end table close parentheses end cell end tablespace 

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

I. Ridha

Mahasiswa/Alumni Universitas Negeri Surabaya

Terakhir diupdate 06 Oktober 2021

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