Given ((a + b(√(cx))))^(1/3) + ((a − b(√(cx))))^(1/3) = d Determine x in terms of a, b, c and d. Solution: Let A = ((a + b(√(cx))))^(1/3) and B = ((a − b(√(cx))))^(1/3) ⇒ A^3 = a + b(√(cx)) and B^3 = a − b(√(cx)) ⇒ A^3 + B^3 = 2a ⇒ (A + B)[(A + B)^2 − 3AB)] = 2a ⇒ d(d^2 − 3AB) = 2a ⇒ AB = ((d^3 − 2a)/(3d)) ((a + b(√(cx))))^(1/3) × ((a − b(√(cx))))^(1/3) = ((d^3 − 2a)/(3d)) a^2 − b^2 cx = (((d^3 − 2a)^3 )/(27d^3 )) x = (a^2 /(b^2 c)) − (((d^3 − 2a)^3 )/(27b^2 cd^3 ))