Pertanyaan

Diketahui a , b , dan c adalah bilangan riil positif. Jika 4 a b 3 b c = ab ,maka nilai adalah .... (SBM TPA 2015)

Diketahui $a, b,$ dan $c$ adalah bilangan riil positif. Jika $\frac{b c}{4 a b ^{3}} = ab$ , maka nilai adalah .... (SBM TPA 2015)

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Perhatikan perhitungan sebagai berikut! Jadi, jawaban yang tepat adalah A.

Perhatikan perhitungan sebagai berikut!

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator square root of b c end root over denominator fourth root of a b cubed end root end fraction end cell equals cell a b end cell row cell open parentheses b c close parentheses to the power of begin display style 1 half end style end exponent over open parentheses a b cubed close parentheses to the power of begin display style 1 fourth end style end exponent end cell equals cell a b end cell row cell fraction numerator b to the power of begin display style fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction end style end exponent c to the power of 1 half end exponent over denominator a to the power of 1 fourth end exponent b to the power of 3 over 4 end exponent end fraction end cell equals cell a b end cell row cell a to the power of negative 1 fourth end exponent b to the power of fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction minus 3 over 4 end exponent c to the power of blank to the power of 1 half end exponent end exponent end cell equals cell a b end cell row cell a to the power of negative 1 fourth end exponent b to the power of fraction numerator begin display style 2 end style over denominator begin display style 4 end style end fraction minus 3 over 4 end exponent c to the power of blank to the power of 1 half end exponent end exponent end cell equals cell a b end cell row cell a to the power of negative 1 fourth end exponent b to the power of negative 1 fourth end exponent c to the power of blank to the power of 1 half end exponent end exponent end cell equals cell a b end cell row cell open parentheses a b close parentheses to the power of negative 1 fourth end exponent c to the power of blank to the power of 1 half end exponent end exponent end cell equals cell a b end cell row cell c to the power of blank to the power of 1 half end exponent end exponent end cell equals cell fraction numerator a b over denominator open parentheses a b close parentheses to the power of negative 1 fourth end exponent end fraction end cell row cell c to the power of blank to the power of 1 half end exponent end exponent end cell equals cell open parentheses a b close parentheses open parentheses a b close parentheses to the power of 1 fourth end exponent end cell row cell c to the power of blank to the power of 1 half end exponent end exponent end cell equals cell open parentheses a b close parentheses to the power of 1 plus 1 fourth end exponent end cell row cell c to the power of blank to the power of 1 half end exponent end exponent end cell equals cell open parentheses a b close parentheses to the power of 5 over 4 end exponent end cell row cell open parentheses c to the power of blank to the power of 1 half end exponent end exponent close parentheses squared end cell equals cell open parentheses open parentheses a b close parentheses to the power of 5 over 4 end exponent close parentheses squared end cell row c equals cell open parentheses a b close parentheses to the power of 5 over 4 times 2 end exponent end cell row c equals cell open parentheses a b close parentheses to the power of 5 over 2 end exponent end cell end table end style$

Jadi, jawaban yang tepat adalah A.

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5.0 (2 rating)

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