XY+X+Y=23,X^2Y+XY^2=120,求x^3+y^3谢谢了,

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XY+X+Y=23,X^2Y+XY^2=120,求x^3+y^3谢谢了,XY+X+Y=23,X^2Y+XY^2=120,求x^3+y^3谢谢了,XY+X+Y=23,X^2Y+XY^2=120,求x^3

XY+X+Y=23,X^2Y+XY^2=120,求x^3+y^3谢谢了,
XY+X+Y=23,X^2Y+XY^2=120,求x^3+y^3谢谢了,

XY+X+Y=23,X^2Y+XY^2=120,求x^3+y^3谢谢了,
首先我们假设a=x+y,b=xy,那么a+b=23,ab=120 所以求得a=15 b=8或者a=8 b=15 而x^3+y^3 =(x+y)^3-3xy(x+y) =a^3-3ab 所以x^3+y^3=8^3-3*120=152 或者x^3+y^3=15^3-3*120=3015