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

a(b² + c²) = c(b² + c²)

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a(b² + c²) = c(a² + b²)

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a²(b + c) = c²(a + b)

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none of these

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Solution

The correct option is B a(b² + c²) = c(a² + b²)
$\frac{b}{a} = \frac{c}{b} \Rightarrow= \frac{b^{2}}{a^{2}} = \frac{c^{2}}{b^{2}}$

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

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

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

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