If x, y are two positive integers such that x+y=20 and the maximum value of x^3 y is k at x= , y= then k ^2 ^2 =

Step-by-step solution

x+y=20 x 3 + x 3 + x 3 +y 4 [ ( x 3 )^3 y ]^ 1 / 4 5 ( x^3 y 3^3 )^ 1 4 x^5 y 27 625 x^3 y 27 625 k=27 625 at x 3 =y 4 y=20 y=5= , x=15= k ^2 ^2 = 27 625 15^2 5^2 =3=