求不定方程x^2+y^2+x^2y^2+10xy+16=0的解(x,y为实数)

2024-12-28 09:58:41
推荐回答(1个)
回答1:

x²+y²+x²y²+10xy+16=0
<=> (x²+y²+2xy)+(x²y²+8xy+16)=0
<=>(x+y)²+(xy+4)²=0

=> x+y=0且xy=-4
解上面的两个方程得到x=2,y=-2,或x=-2,y=2