Question

If x^(2)+y^(2)=89 and xy=40,then find the value of x^(3)+y^(3).

Answer 1

X^2 + y^2 = 89 ------(1)

xy = 40 ------(2)


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

=> (x+y) ^2 = 89 + 80

=> (x+y) ^2 = 169

=> x + y = 13 ------(3)

Now,

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

= ( 13)(89 - 40)

= 13 × 49

= 637