Q8 of 176 Page 20

If a, b, c are in G.P., prove that :

a(b2 + c2) = c(a2 + b2)

Now, as a,b,c are in GP.


Using the idea of geometric mean we can write –


∴ b2 = ac …(1)


Put in the LHS of the given equation to be proved –


LHS = a(ac + c2) {putting b2 = ac}


⇒ LHS = a2c + ac2


⇒ LHS = c(a2 + ac)


Again put ac = b2


⇒ LHS = c(a2 + b2) = RHS


∴ L.H.S = R.H.S


Hence proved


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