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Division of Polynomials

If ax = b;b...

Question

If $a^{x} = b; b^{y} = c; c^{z} = a$ & $2 x^{2} + 5 y^{2} + z^{2} - 6 x y + 2 y z - 2 x z = 0$ then value of $x^{3} + 3 y^{3} + 5 z^{3}$ is

A

0

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B

1

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C

8

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D

12

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Solution

The correct option is D 8
$a^{x y z} = a \Rightarrow x y z = 1$ ...(i)
$(y + z - x)^{2} + (x - 2 y)^{2} = 0$
so , $y + z - x = 0$ & $x = 2 y$
so , $x = 2 y$ & $z = y$
so , $2 y^{3} = z^{3} = \frac{1}{2}$ & $z = y$
$\Rightarrow x^{3} + 3 y^{3} + 5 z^{3} = 8$

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