Pertanyaan

Jika maka nilai 2 a − b + 2 c adalah ....

Jika $fraction numerator open parentheses 4 square root of x to the power of 18 y to the power of 9 end root minus 2 square root of 2 open parentheses x to the power of 6 y cubed close parentheses cubed end root close parentheses open parentheses 4 square root of x to the power of 18 y to the power of 9 end root plus 2 square root of 2 open parentheses x to the power of 6 y cubed close parentheses cubed end root close parentheses over denominator 4 square root of square root of 256 x to the power of 28 y to the power of 30 end root end root end fraction equals 2 to the power of a x to the power of b y to the power of c comma$ maka nilai $2 a - b + 2 c$ adalah ....

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

Ingat bahwa sehingga diperoleh hasil perhitungan sebagai berikut. Karena maka didapat dan Dengan demikian,nilai adalah sebagai berikut. Jadi, jawaban yang tepat adalah B.

Ingat bahwa open parentheses a plus b close parentheses open parentheses a minus b close parentheses equals a squared minus b squared sehingga diperoleh hasil perhitungan sebagai berikut.

$fraction numerator open parentheses 4 square root of x to the power of 18 y to the power of 9 end root minus 2 square root of 2 open parentheses x to the power of 6 y cubed close parentheses cubed end root close parentheses open parentheses 4 square root of x to the power of 18 y to the power of 9 end root plus 2 square root of 2 open parentheses x to the power of 6 y cubed close parentheses cubed end root close parentheses over denominator 4 square root of square root of 256 x to the power of 28 y to the power of 30 end root end root end fraction equals fraction numerator open parentheses 4 square root of x to the power of 18 y to the power of 9 end root minus 2 square root of 2 x to the power of 18 y to the power of 9 end root close parentheses open parentheses 4 square root of x to the power of 18 y to the power of 9 end root plus 2 square root of 2 x to the power of 18 y to the power of 9 end root close parentheses over denominator 4 square root of open parentheses 16 squared x to the power of 28 y to the power of 30 close parentheses to the power of 1 half end exponent end root end fraction equals fraction numerator open parentheses 4 square root of x to the power of 18 y to the power of 9 end root close parentheses squared minus open parentheses 2 square root of 2 x to the power of 18 y to the power of 9 end root close parentheses squared over denominator 4 square root of 16 x to the power of 14 y to the power of 15 end root end fraction equals fraction numerator 16 x to the power of 18 y to the power of 9 minus 8 x to the power of 18 y to the power of 9 over denominator 4 open parentheses 16 x to the power of 14 y to the power of 15 close parentheses to the power of 1 half end exponent end fraction equals fraction numerator left parenthesis 16 minus 8 right parenthesis x to the power of 18 y to the power of 9 over denominator 4 open parentheses 4 squared x to the power of 14 y to the power of 15 close parentheses to the power of 1 half end exponent end fraction equals fraction numerator 8 x to the power of 18 y to the power of 9 over denominator 4 open parentheses 4 x to the power of 7 y to the power of 15 over 2 end exponent close parentheses end fraction equals fraction numerator 2 x to the power of 18 y to the power of 9 over denominator 4 x to the power of 7 y to the power of 15 over 2 end exponent end fraction equals 1 half x to the power of 18 minus 7 end exponent y to the power of 9 minus 15 over 2 end exponent equals 2 to the power of negative 1 end exponent x to the power of 11 y to the power of 3 over 2 end exponent$

Karena $fraction numerator open parentheses 4 square root of x to the power of 18 y to the power of 9 end root minus 2 square root of 2 open parentheses x to the power of 6 y cubed close parentheses cubed end root close parentheses open parentheses 4 square root of x to the power of 18 y to the power of 9 end root plus 2 square root of 2 open parentheses x to the power of 6 y cubed close parentheses cubed end root close parentheses over denominator 4 square root of square root of 256 x to the power of 28 y to the power of 30 end root end root end fraction equals 2 to the power of a x to the power of b y to the power of c comma$ maka didapat a equals negative 1 comma b equals 11 comma dan c equals 3 over 2.

Dengan demikian, nilai adalah sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 a minus b plus 2 c end cell equals cell 2 open parentheses negative 1 close parentheses minus 11 plus 2 open parentheses 3 over 2 close parentheses end cell row blank equals cell negative 2 minus 11 plus 3 end cell row blank equals cell negative 10 end cell end table

Jadi, jawaban yang tepat adalah B.