Question

if a/b = c/d = e=f
prove that

(b² + d² + f²) (a² + c² + e²) = (ab + cd + ef)​

Answer 1

Let a/b = c/d = e/f = k

Then, a = bk, c = dk and e = fk

(ab + cd + ef)² = (bk.b + dk.d + fk.f)² = k²(b² + d² + f²)²

(b² + d² + f²) (a² + c² + e²) = (b²k² +d²k² + f²k²)(b² + d² + f²) = k²(b² + d² + f²)

Hence, (b² + d² + f²) (a² + c² + e²) = (ab + cd + ef) [Proved]