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