Question

if x+y =6 xy=2 find x3 -y3​

Answer 1

(x+y)^2 = x^2 + y^2 +2 xy

        36= x^2 + y^2 + 4

 

         x^2 + y^2 = 32

(x-y)^2 = x^2 + y^2 - 2xy

          = 32 - 4

(x-y)^2 = 28 = > x-y = 2 √7

x^3 - y^3 = (x-y)(x^2 + y^2 + xy)

               =(2√7) x ( 2 + 32 )

               = 2 x 34 x √7

               = 68 x√7

               = 68 x 2.465 = 167.62