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Pertanyaan

Jika ∣ ∣ ​ ∣ a ∣ − ∣ ∣ ​ a b ​ ∣ ∣ ​ ∣ ∣ ​ 2 = 1 dan a 2 + a 2 b 2 ​ = 13 , maka nilai dari ∣ ∣ ​ a + a 6 ​ ∣ ∣ ​ adalah ....

Jika  dan , maka nilai dari  adalah ....

  1. 1space 

  2. 5space 

  3. 6space 

  4. 13space 

  5. 25space 

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D. Natalia

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

jawaban yang tepat adalah B.

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Pembahasan

DiketahuiJika dan , maka didapat perhitungan sebagai berikut. Selanjutnya, perhatikan perhitungan berikut! Jadi, jawaban yang tepat adalah B.

Diketahui Jika open vertical bar open vertical bar a close vertical bar minus open vertical bar b over a close vertical bar close vertical bar squared equals 1 dan a squared plus b squared over a squared equals 13, maka didapat perhitungan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar open vertical bar a close vertical bar minus open vertical bar b over a close vertical bar close vertical bar squared end cell equals cell open parentheses open vertical bar a close vertical bar minus open vertical bar b over a close vertical bar close parentheses squared end cell row 1 equals cell open vertical bar a close vertical bar squared minus 2 open vertical bar a close vertical bar open vertical bar b over a close vertical bar plus open vertical bar b over a close vertical bar squared end cell row 1 equals cell open vertical bar a close vertical bar squared plus open vertical bar b over a close vertical bar squared minus 2 open vertical bar a close vertical bar open vertical bar b over a close vertical bar end cell row 1 equals cell a squared plus open parentheses b over a close parentheses squared minus 2 open vertical bar a times b over a close vertical bar end cell row 1 equals cell a squared plus b squared over a squared minus 2 open vertical bar b close vertical bar end cell row 1 equals cell 13 minus 2 open vertical bar b close vertical bar end cell row cell 2 open vertical bar b close vertical bar end cell equals 12 row cell open vertical bar b close vertical bar end cell equals 6 end table

Selanjutnya, perhatikan perhitungan berikut!

table attributes columnalign right center left columnspacing 0px end attributes row cell a squared plus b squared over a squared minus 2 open vertical bar b close vertical bar end cell equals 1 row cell open vertical bar a close vertical bar squared plus open vertical bar b close vertical bar squared over open vertical bar a close vertical bar squared minus 2 open vertical bar b close vertical bar end cell equals 1 row cell open vertical bar a close vertical bar squared plus 6 squared over open vertical bar a close vertical bar squared minus 2 open parentheses 6 close parentheses end cell equals 1 row cell open vertical bar a close vertical bar squared plus 36 over open vertical bar a close vertical bar squared minus 12 end cell equals 1 row cell open vertical bar a close vertical bar squared plus 36 over open vertical bar a close vertical bar squared end cell equals 13 row cell a squared plus 36 over a squared end cell equals 13 row cell a squared plus 36 over a squared plus 12 end cell equals cell 13 plus 12 end cell row cell open parentheses a plus 6 over a close parentheses squared end cell equals 25 row cell a plus 6 over a end cell equals cell plus-or-minus square root of 25 end cell row cell a plus 6 over a end cell equals cell plus-or-minus 5 end cell row cell open vertical bar a plus 6 over a close vertical bar end cell equals 5 end table

Jadi, jawaban yang tepat adalah B.

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