If a, b, c are in G.P, then

$a (b^{2} + c^{2}) = c (b^{2} + c^{2})$

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$a (b^{2} + c^{2}) = c (a^{2} + b^{2})$

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$a^{2} (b + c) = c^{2} (a + b)$

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none of these

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Solution

The correct option is B
$a (b^{2} + c^{2}) = c (a^{2} + b^{2})$

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

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

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

$∴ c (b^{2} + a^{2}) = a (c^{2} + b^{2})$

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