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Question
If a, b, c are in G.P., prove that:
a (b2 + c2) = c (a2 + b2)
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Solution
a, b and c are in G.P.
\[\therefore b^2 = ac\] .......(1)
\[\text {LHS } = a\left( b^2 + c^2 \right)\]
\[ = a b^2 + a c^2 \]
\[ = a\left( ac \right) + c\left( b^2 \right) \left[ \text { Using } (1) \right]\]
\[ = c\left( a^2 + b^2 \right) = \text { RHS }\]
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