If $a, b, c$ are in G.P ., then $a (b^{2} + c^{2})$ is

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Solution

Given $a, b, c$ are in GP
So $b^{2} = a c . . (i)$
$a (b^{2} + c^{2}) = a (a c + c^{2}) = a (a c) + a c^{2} = a^{2} c + a c = c (a^{2} + b^{2}) a (b^{2} + c^{2}) = c (a^{2} + b^{2})$
Hence, the value of $a (b^{2} + c^{2}) i s c (a^{2} + b^{2})$

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