if a, b, c are in G.P., prove that a(b2 + c2) = c(a2 + b2)

if a, b, c are in G.P., prove that a(b2 + c2) = c(a2 + b2)

Asked by Sakshi | 1 year ago |  72
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1 Answer

Solution :-

a(b2 + c2) = c(a2 + b2)

Given that a, b, c are in GP.

By using the property of geometric mean,

b2 = ac

Let us consider LHS: a(b2 + c2)

Now, substituting b2 = ac, we get

a(ac + c2)

a2c + ac2

c(a2 + ac)

Substitute ac = b2 we get,

c(a2 + b2) = RHS

LHS = RHS

Hence proved.

Answered by Aaryan | 1 year ago
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