Question

if `a/b = c/d` prove that each of the given ratio is equal to: `((8a^3 + 15c^3)/(8b^3 + 15d^3))^(1/3)`

Answer 1

Let `a/b = c/b = k`

Then a =  bk and c = dk

`((8a^3 + 15c^3)/(8b^3 + 15d^3))^(1/3) =  [(8(bk)^3 + 15(dk)^3)/(8b^3 + 15d^3)]^(1/3) = [(k^3(8b^3 + 15d^3))/(8b^3 + 15d^3))]^(1/3) = k` = each given ratio