坐等！！

解出来 立马粉他

(x+1/x)(y+1/y)=4
设
x+1/x = a
y+1/y = b
那么ab = 4
但是a = x + 1/x >= 2 (或a<=-2)
b = y + 1/y >= 2 或(b<=-2)
所以a = b = 2或 a = b = -2
所以x = y = 1或 x = y = -1
x^2 - 3y + 1 = -1或5

∵ (x²+1)(y²+1)=4xy
∴ x²y²+x²+y²+1-4xy=0
∴ x²y²-2xy+1+x²-2xy+y²=0
∴ (x²y²-2xy+1)+(x²-2xy+y²)=0
∴ (xy-1)²+(x-y)²=0
∴ (xy-1)²=0 且 (x-y)²=0
∴ xy=1 且 x=y
∴ x=y=1
∴ x²-3y+1 = 1²-3×1+1=-1

∵ (x²+1)(y²+1)=4xy
∴ x²y²+x²+y²+1-4xy=0
∴ x²y²-2xy+1+x²-2xy+y²=0
∴ (x²y²-2xy+1)+(x²-2xy+y²)=0
∴ (xy-1)²+(x-y)²=0
∴ (xy-1)²=0 且 (x-y)²=0
∴ xy=1 且 x=y
∴ x=y=1 或 x=y=-1
∴ x²-3y+1 = 1²-3×1+1=-1 或 x²-3y+1 = (-1)²-3×(-1)+1=5

特殊值法

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