Question

a/b=c/d=e/f prove that (ab+cd+ef)^2=(a^2+c^2+e^2)(b^2+d^2+f^2)

Answer 1

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

a = bk, c = dk and e = fk

L.H.S. = (ab + cd + ef)2

= (bk.b + dk.d + fk.f)2

= k2(b2 + d2 + f2)2

R.H.S. = (a2 + c2 + e2)(b2 + d2 + f2)

= (b2k2 + d2k2 + f2k2)(b2 + d2 + f2)

= k2(b2 + d2 + f2)(b2 + d2 + f2)

= k2(b2 + d2 + f2)2

L.H.S. = R.H.S.

Hence proved