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If a,b,c, and d are in G.P., show that (...

If a,b,c, and d are in G.P., show that `(ab+bc+cd)^(2)=(a^(2)+b^(2)+c^(2))(b^(2)+c^(2)+d^(2))`.

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To show that \( (ab + bc + cd)^2 = (a^2 + b^2 + c^2)(b^2 + c^2 + d^2) \) given that \( a, b, c, d \) are in geometric progression (G.P.), we can follow these steps: ### Step 1: Express \( b, c, d \) in terms of \( a \) and the common ratio \( r \) Since \( a, b, c, d \) are in G.P., we can express: - \( b = ar \) - \( c = ar^2 \) - \( d = ar^3 \) ...
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