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Q.

If $y^{2} + z^{2} = 3 y z, z^{2} + x^{2} = 8 x z, x^{2} + y^{2} = 4 x y$ then the value of $\frac{y^{2}}{x z} + \frac{x z}{y^{2}} =$

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a

2

b

3

c

4

d

5

answer is C.

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Detailed Solution

$\begin{array}{l} \frac{y}{z} + \frac{z}{y} = 3 \to (1) \\ \frac{z}{x} + \frac{x}{z} = 8 \to (2) \\ \frac{x}{y} + \frac{y}{x} = 4 \to (3) \\ (1) \times (3) \Rightarrow \frac{x}{z} + \frac{y^{2}}{x z} + \frac{x z}{y^{2}} + \frac{z}{x} = 12 \\ \Rightarrow \frac{y^{2}}{x z} + \frac{x z}{y^{2}} = 12 - 8 = 4 \end{array}$

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