Q4 of 59 Page 77

If (a + b+ c)(a –b + c) = a2 + b2 + c2 , show that a, b, c are in continued proportion.

Given: (a + b+ c)(a –b + c) = a2 + b2 + c2


⇒ a2 –ab + ac + ab - b2 + bc + ca – bc + c2 = a2 + b2 + c2


⇒ a2 –ab + ac + ab - b2 + bc + ca – bc + c2 - a2 - c2= b2 + b2


⇒ 2ac = 2b2


⇒ b2 = ac


∴ a, b, c are in continued proportion.


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