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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.

Pembahasan

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

Misalkan

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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