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