Question

若x+y=2,且(x+2)(y+2)=5,求x^3+y^3的值

Answer 1

x+y=2,且(x+2)(y+2)=5,求x^3+y^3的值

2(x+y) + xy + 4 = 5

xy = 5-4-4 = -3

x(2-x) =-3

x²-2x -3 = 0

(x-3)(x+1)=0

x=3 或者 -1

y= -1 或者 3 代入

x^3+y^3

= -1 + 27

= 26