
### Instruction: help me answer this question If a, b, c and d are in G.P., show that (a^2 + b^2 + c^2)(b^2 + c^2 + d^2) = (ab + bc + cd)^2, think step by step
### Assistant: As a, b, c, and d are in G.P., we have b^2 = ac and c^2 = bd. We first express the given expression as a quadratic in ac, find its roots using the quadratic formula, and then show that these roots are indeed b^2 and d^2, thus verifying the identity. , The answer is (a^2 + b^2 + c^2)(b^2 + c^2 + d^2) = (ab + bc + cd)^2
