Question

if a, b, c are in continued proportion prove(a+b+c) (a-b+c) =a^2+b^2+c^2

Answer 1

Answer:

LHS

(a+b+c) (a-b+c) = a^2 -b^2 + c^2 -ab +ab + bc - bc +ac+ac

= a^2-b^2+c^2 + ac+ac

= a^2-b^2+c^2 + b^2+b^2 (as b^2 = ac )

=a^2+b^2+c^2

RHS

a^2+b^2+c^2

proved