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Question
If a, b, c are in G.P., prove that:
(a + 2b + 2c) (a − 2b + 2c) = a2 + 4c2.
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Solution
a, b and c are in G.P.
\[\therefore b^2 = ac\] .......(1)
\[\text { LHS }= \left( a + 2b + 2c \right)\left( a - 2b + 2c \right)\]
\[ = a^2 - 4 b^2 + 4 c^2 + 4ac\]
\[ = a^2 - 4ac + 4 c^2 + 4ac \left[ \text { Using }(1) \right]\]
\[ = a^2 + 4 c^2 = \text { RHS }\]
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