The values of x which satisfy $y z = a^{2}, z x = b^{2}, x y = c^{2}$ are.

\pm c a / b

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\pm a / b c

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\pm b c / a

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\pm b / c a

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Solution

The correct option is C $\pm b c / a$
$y z = a^{2}$

$\Rightarrow z = \frac{a^{2}}{y}$
$x z = b^{2}$

$\Rightarrow x \frac{a^{2}}{y} = b^{2}$

$\Rightarrow y = \frac{a^{2} x}{b^{2}}$

$x y = c^{2}$

$\Rightarrow x \cdot \frac{a^{2} x}{b^{2}} = c^{2}$

$\Rightarrow \frac{a^{2} x^{2}}{b^{2}} = c^{2}$

$\Rightarrow x^{2} = \frac{b^{2} c^{2}}{a^{2}}$

$\Rightarrow x = \frac{\pm b c}{a}$

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