Question

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

If `a/c = c/d = e/f` prove that (a³ + c³)² : (b³ + d³)² = e⁶ : f⁶

Answer 1

`a/c = c/d = e/f` = k(say)

∴ a = bk, c = dk, e =fk

L.H.S.

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

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

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

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

= k⁶

R.H.S. = `e^6/f^6`

= `f^6k^6/f^6`

= k⁶

∴ L.H.S. = R.H.S.