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Tentukan nilai x yang memenuhi pertidaksamaan berikut. 2. x2+6x​>∣2x−7∣

Pertanyaan

Tentukan nilai x yang memenuhi pertidaksamaan berikut.

2. square root of x squared plus 6 x end root greater than open vertical bar 2 x minus 7 close vertical bar 

S. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

nilai x yang memenuhi pertidaksamaan square root of x squared plus 6 x end root greater than open vertical bar 2 x minus 7 close vertical bar adalah Error converting from MathML to accessible text..

Pembahasan

Ingat bahwa:

Nilai mutlak memiliki sifat open vertical bar a close vertical bar squared equals a squared dan pada bentuk akar berlaku open parentheses square root of a close parentheses squared equals a.

table attributes columnalign right center left columnspacing 0px end attributes row cell square root of x squared plus 6 x end root end cell greater than cell open vertical bar 2 x minus 7 close vertical bar end cell row cell open parentheses square root of x squared plus 6 x end root close parentheses squared end cell greater than cell open parentheses open vertical bar 2 x minus 7 close vertical bar close parentheses squared end cell row cell x squared plus 6 x end cell greater than cell open parentheses 2 x minus 7 close parentheses squared end cell row cell x squared plus 6 x end cell greater than cell 4 x squared minus 28 x plus 49 end cell row cell x squared minus 4 x squared plus 6 x plus 28 x minus 49 end cell greater than 0 row cell negative 3 x squared plus 34 x minus 49 end cell greater than 0 row cell 3 x squared minus 34 x plus 49 end cell less than 0 end table

Ubahlah menjadi bentuk persamaan kuadrat dan carilah akar-akarnya menggunakan rumus

x subscript 1 comma 2 end subscript equals fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction

sehingga diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 comma 2 end subscript end cell equals cell fraction numerator 34 plus-or-minus square root of left parenthesis 34 right parenthesis squared minus 4 left parenthesis 3 right parenthesis left parenthesis 49 right parenthesis end root over denominator 2 left parenthesis 3 right parenthesis end fraction end cell row blank equals cell fraction numerator 34 plus-or-minus square root of 1156 minus 558 end root over denominator 6 end fraction end cell row blank equals cell fraction numerator 34 plus-or-minus square root of 598 over denominator 6 end fraction end cell end table

Jadi, nilai x yang memenuhi pertidaksamaan square root of x squared plus 6 x end root greater than open vertical bar 2 x minus 7 close vertical bar adalah Error converting from MathML to accessible text..

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