(x2+1)(y2+1)=4xy,求代数式x2-5y+1的值

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(x2+1)(y2+1)=4xy,求代数式x2-5y+1的值
(x2+1)(y2+1)=4xy,求代数式x2-5y+1的值

(x2+1)(y2+1)=4xy,求代数式x2-5y+1的值
(x²+1)(y²+1)=4xy
x²y²+x²+y²+1=4xy
(x²y²-2xy+1)+(x²-2xy+y²)=0
(xy-1)²+(x-y)²=0
所以xy-1=0,x=y
解得x=y=1或x=y=-1
x²-5y+1=1-5+1=-3
或
x²-5y+1=1+5+1=7

(x2+1)(y2+1)=4xy
x^2y^2+x^2+y^2+1=4xy
x^2y^2-2xy+1+x^2+y^2-2xy=0
(xy-1)^2+(x-y)^2=0
xy-1=0,x=y
x=1,y=1或x=-1,y=-1
x^2-5y+1=-3或7

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