Question

If `a/b = c/d = e/f`, prove that: `(a^2 + c^2)^3/(b^2 + d^2)^3 = e^6/f^6`

Answer 1

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

a = bk, c = dk, e = fk

L.H.S.

= `(a^2 + c^2)^3/(b^2 + d^2)^3`

= `((bk)^2 + (dk)^2)^3/(b^2 + d^2)^3`

= `(b^2k^2 + d^2k^2)^3/(b^2 + d^2)^3`

= `[k^2(b^2 + d^2)]^3/(b^2 + d^2)^3`

= `(k^6(b^2 + d^2)^3)/(b^2 + d^2)^3`

= k⁶

R.H.S.

= `e^6/f^6`

= `(fk)^6/f^6`

= `(f^6k^6)/f^6`

= k⁶

L.H.S. = R.H.S.