问题
填空题
若抛物线y=2x2-4x+1与x轴两交点分别是(x1,0),(x2,0),则x12+x22=______.
答案
由题意得:y=2x2-4x+1与x轴两交点分别是(x1,0),(x2,0),
∴2x2-4x+1=0,
∴x1+x2=2,x1•x2=
,1 2
∴x12+x22=x12+x22+2x1x2-2x1x2=(x1+x2)2-2x1x2=4-2×
=3.1 2
若抛物线y=2x2-4x+1与x轴两交点分别是(x1,0),(x2,0),则x12+x22=______.
由题意得:y=2x2-4x+1与x轴两交点分别是(x1,0),(x2,0),
∴2x2-4x+1=0,
∴x1+x2=2,x1•x2=
,1 2
∴x12+x22=x12+x22+2x1x2-2x1x2=(x1+x2)2-2x1x2=4-2×
=3.1 2
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