已知抛物线y=X2-(k-1)x-k-1与x轴的交点为A和B,顶点为C,求三角形ABC的面积的最小值.
人气:215 ℃ 时间:2019-08-20 18:59:33
解答
设A(x1,0) B(x2,0),则满足x1+x2=k-1,x1x2=-k-1故|x1-x2|=√[(k-1)^2+4(k+1)]=√(k^2+2k+5)由于y=X2-(k-1)x-k-1=[x-(k-1)/2]^2-(k^2+2k+5)/4故顶点的纵坐标为-(k^2+2k+5)/4,令t=k^2+2k+5,三角形ABC的面积为1/2 ...
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