已知X-Y不等于0,X^2-X=7,Y^2-Y=7,求X^3+Y^3+X^2Y+XY^2的值

设X,Y为方程：xx-x-7=0的根X+Y=1,XY=-7.XX+YY=(X+Y)(X+Y)-2XY=1+14=15XXX+YYY+XXY+XYY=X(XX+YY)+Y(XX+YY)=(X+Y)(XX+YY)=1*15=15
那下面这一步明白么,
x^3+y^3+x^2y+xy^2
=(x+y)(x^2+y^2-xy)+xy(x+y)
=1*(x^2+y^2-xy)+xy*1
=x^2+y^2
再根据X^2-X=7,Y^2-Y=7
得出X^2=7+x y^2=7+y
带入x^2+y^2就行了了