Question

 If `a/b = c/d = e/f`, prove that: `a^2/b^2 + c^2/d^2 + e^2/f^2 = (ac)/(bd) + (ce)/(df) + (ae)/(bf)`

Answer 1

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

a = bk, c = dk, e = fk

L.H.S.

= `a^2/b^2 + c^2/d^2 + e^2/f^2`

= `(bk)^2/b^2 + (dk)^2/d^2 + (fk)^2/f^2`

= `(b^2k^2)/b^2 + (d^2k^2)/d^2 + (f^2k^2)/f^2`

= k² + k² + k²

= 3k²

R.H.S.

= `(ac)/(bd) + (ce)/(df) + (ae)/(bf)`

= `((bk)(dk))/(bd) + ((dk)(fk))/(df) + ((bk)(fk))/(bf)`

= `(bdk^2)/(bd) + (dfk^2)/(df) + (bfk^2)/(bf)`

= k² + k² + k²

= 3k²

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