已知(X^2+1)(Y^2+1)=4XY,求代数式X^2-3Y+2的值

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已知(X^2+1)(Y^2+1)=4XY,求代数式X^2-3Y+2的值已知(X^2+1)(Y^2+1)=4XY,求代数式X^2-3Y+2的值已知(X^2+1)(Y^2+1)=4XY,求代数式X^2-3

已知(X^2+1)(Y^2+1)=4XY,求代数式X^2-3Y+2的值
已知(X^2+1)(Y^2+1)=4XY,求代数式X^2-3Y+2的值

已知(X^2+1)(Y^2+1)=4XY,求代数式X^2-3Y+2的值
(X^2+1)(Y^2+1)=4XY
x^2y^2+(x^2+y^2)+1-4xy=0
(x^2y^2-2xy+1)+(x^2-2xy+y^2)=0
(xy-1)^2+(x-y)^2=0
平方数非负
要使等式成立只能
xy-1=0
x-y=0
x=1,y=1 或者x=-1,y=-1
X^2-3Y+2
=1-3+2
=0
或者
X^2-3Y+2
=1+3+2
=6

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