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Hasil dari ( 2 ​ + 3 ​ + 5 ​ ) ( 2 ​ + 3 ​ − 5 ​ ) ( 2 ​ − 3 ​ + 5 ​ ) ( − 2 ​ + 3 ​ + 5 ​ ) adalah ....

Hasil dari  adalah ....

  1. begin mathsize 14px style 2 square root of 5 end style 

  2. begin mathsize 14px style 2 square root of 6 end style 

  3. begin mathsize 14px style 10 end style 

  4. begin mathsize 14px style 24 end style 

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S. Difhayanti

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. Dr. Hamka

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

jawaban yang tepat adalah D.

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Pembahasan

Misalkan Ingat sifat berikut. Perhatikan bahwa Kemudian Dengan demikian, Jadi, jawaban yang tepat adalah D.

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begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row a equals cell open parentheses square root of 2 plus square root of 3 plus square root of 5 close parentheses end cell row b equals cell open parentheses square root of 2 plus square root of 3 minus square root of 5 close parentheses end cell row c equals cell open parentheses square root of 2 minus square root of 3 plus square root of 5 close parentheses end cell row d equals cell open parentheses negative square root of 2 plus square root of 3 plus square root of 5 close parentheses end cell end table end style 

Ingat sifat berikut.

begin mathsize 14px style open parentheses square root of x plus square root of y close parentheses open parentheses square root of x minus square root of y close parentheses equals open parentheses square root of x close parentheses squared minus open parentheses square root of y close parentheses squared open parentheses square root of x plus square root of y close parentheses squared equals open parentheses x plus y close parentheses plus 2 square root of x y end root open parentheses square root of x minus square root of y close parentheses squared equals open parentheses x plus y close parentheses minus 2 square root of x y end root end style 

Perhatikan bahwa

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a b end cell equals cell open parentheses square root of 2 plus square root of 3 plus square root of 5 close parentheses open parentheses square root of 2 plus square root of 3 minus square root of 5 close parentheses end cell row blank equals cell open parentheses open parentheses square root of 2 plus square root of 3 close parentheses plus square root of 5 close parentheses open parentheses open parentheses square root of 2 plus square root of 3 close parentheses minus square root of 5 close parentheses end cell row blank equals cell open parentheses square root of 2 plus square root of 3 close parentheses squared minus open parentheses square root of 5 close parentheses squared end cell row blank equals cell open parentheses open parentheses 2 plus 3 close parentheses plus 2 square root of 2 cross times 3 end root close parentheses minus 5 end cell row blank equals cell 5 plus 2 square root of 6 minus 5 end cell row blank equals cell 2 square root of 6 end cell end table end style 

Kemudian

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell c d end cell equals cell open parentheses square root of 2 minus square root of 3 plus square root of 5 close parentheses open parentheses negative square root of 2 plus square root of 3 plus square root of 5 close parentheses end cell row blank equals cell left parenthesis square root of 2 minus square root of 3 plus square root of 5 right parenthesis open parentheses negative 1 close parentheses left parenthesis square root of 2 minus square root of 3 minus square root of 5 right parenthesis end cell row blank equals cell negative open parentheses open parentheses square root of 2 minus square root of 3 close parentheses plus square root of 5 close parentheses open parentheses open parentheses square root of 2 minus square root of 3 close parentheses minus square root of 5 close parentheses end cell row blank equals cell negative open parentheses open parentheses square root of 2 minus square root of 3 close parentheses squared minus open parentheses square root of 5 close parentheses squared close parentheses end cell row blank equals cell negative open parentheses open parentheses open parentheses 2 plus 3 close parentheses minus 2 square root of 2 cross times 3 end root close parentheses minus 5 close parentheses end cell row blank equals cell negative open parentheses 5 minus 2 square root of 6 minus 5 close parentheses end cell row blank equals cell negative open parentheses negative 2 square root of 6 close parentheses end cell row blank equals cell 2 square root of 6 end cell end table end style 

Dengan demikian,

begin mathsize 14px style open parentheses square root of 2 plus square root of 3 plus square root of 5 close parentheses open parentheses square root of 2 plus square root of 3 minus square root of 5 close parentheses open parentheses square root of 2 minus square root of 3 plus square root of 5 close parentheses open parentheses negative square root of 2 plus square root of 3 plus square root of 5 close parenthesesequals a b c dequals open parentheses a b close parentheses open parentheses c d close parenthesesequals open parentheses 2 square root of 6 close parentheses open parentheses 2 square root of 6 close parenthesesequals 4 cross times 6equals 24 end style 

Jadi, jawaban yang tepat adalah D.

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