Question

ifx+y=5 and x^2+y^2=13 then find x^3+y^3

Answer 1

x+y = 5

(x+y)² = 5²

or x² + y² + 2xy = 25

or 13 + 2xy = 25

or 2xy = 25 - 13

or 2xy = 12

or xy = 12/2 = 6.

(x+y)³ = x³ + y³ + 3xy(x+y)

or (5)³ = x³ + y³ + 3(6)(5)

or 125 = x³ + y³ + 90

or x³ + y³ = 125 - 90 = 35.

So, x³ + y³ = 35.