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求函数y=根号下(x^2-4x+5)+根号下（x^2-2x+10)的最小值

2025-02-13 00:17:00

推荐回答（1个）

回答1：

函数解析式可化为y=√[(x-2)²+(0-1)²]+√[(x-1)²+(0+3)²].易知,该式的几何意义即是x轴上的一动点P(x,0)到两定点M(2,1),N(1,-3)的距离之和.由“连结两点的所有线中,直线段最短”可知,ymin=|MN|=√17.

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