若|x+y-2|+[2xy-1] 2【这个2是平方】=0,求x2+6xy+y2的值
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若|x+y-2|+[2xy-1] 2【这个2是平方】=0,求x2+6xy+y2的值
若|x+y-2|+[2xy-1] 2【这个2是平方】=0,求x2+6xy+y2的值
若|x+y-2|+[2xy-1] 2【这个2是平方】=0,求x2+6xy+y2的值
∵|x+y-2|+[2xy-1]²=0 |x+y-2|≥0 [2xy-1]²≥0
∴2xy-1=0 2xy=1
x+y-2=0 ( x+y)²=2² x²+2xy+y²=4 x²+y²+1=4 x²+y²=3
x²+6xy+y²=3+1×3=6
因:|x+y-2|+[2xy-1] ^2=0,所以:x+y-2=0,2xy-1=0。即:x+y=2,xy=1/2
所以:x^2+6xy+y^2=(x+y)^2+4xy=2^2+4*(1/2)=4+2=6
x+y=2
xy=1/2
x2+6xy+y2=(x+y)^2+4xy=4+2=6
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