已知x+y=2,xy=a+4,x^3+y^3=36,求a的值

已知x+y=2,xy=a+4,x^3+y^3=36,求a的值
已知x+y=2,xy=a+4,x^3+y^3=36,求a的值

已知x+y=2,xy=a+4,x^3+y^3=36,求a的值
x^3+y^3=(x+y)(x^2-xy+y^2)=(x+y)[(x+y)^2-3xy]
x+y=2,xy=a+4
x^3+y^3=2*(4-3a-12)=36
a=-26/3

x^3+y^3=(x+y)(x^2+y^2-xy)
36=2*((x+y)^2-3xy)
36=2*(4-3(a+4))
a=-26/3

a=-26/3

这里面涉及到x^3，y^3
（x+y）^3=8
x^3+3x^2y+3xy^2+y^3=8
带入x^3+y^3=36即得
36+3x^2 y+3xy^2=8
28+3x^2 y+3xy^2=0
两边同时除以xy
28/xy+3x+3y=0
由已知条件x+y=2,xy=a+4，带入即得
28/（a+4）+6=0
a=-26/3