Question

If `a/b = c/d = e/f`, prove that each ratio is `[(2a^3 + 5c^3 + 7e^3)/(2b^3 + 5d^3 + 7f^3)]^(1/3)`

Answer 1

`a/b = c/d = e/f` = k(say)
∴ a = k, c = dk, e = fk
`[(2a^3 + 5c^3 + 7e^3)/(2b^3 + 5d^3 + 7f^3)]^(1/3)`

= `[(2b^3k^3 + 5d^3k^3 + 7f^3k^3)/(2b^3 + 5d^3 + 7f^3)]^(1/3)`

= `k[(2b^3 + 5d^3 + 7f^3)/(2b^3 + 5d^3 + 7f^3)]^(1/3)` = k
Hence proved.