试题
若|2x+y-1|+(x-2y)2=0,则x2+xy+y2的值为
考点:解二元一次方程组;非负数的性质:绝对值;非负数的性质:偶次方
分析:因为|2x+y-1|+(x-2y)2=0,所以|2x+y-1|≥0,(x-2y)2≥0,据此可解出x、y,再把x、y代入x2+xy+y2即可
解答:解:依题意得:|2x+y-1|=0,(x-2y)2=0
∴2x+y-1=0①,x-2y=0②,
①×2+②,得5x=2,
x=
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则y=
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∴x2+xy+y2=
点评:此题考查的是学生对非负数和二元一次方程组的性质的理解,含绝对值的式子和平方的式子都具有非负性,两个非负的式子相加,则两个非负数的值均为0.
加DB把
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