已知坐標平面內(nèi)兩點A(x,√2—x)和B(√2/2,0),那么這兩點間距離的最小值是0.5
|AB|=√[(x-√2/2)^2+(√2-x)^2]
=√(2x^2-3√2x+2.5)
=√[(√2x-1.5)^2+0.25]
≥√0.25
=0.5這一步怎么配方的 =√[(√2x-1.5)^2+0.25]2x^2=(√2x)^2
3√2x=2*1.5*√2x
1.5^2=2.25
(√2x)^2-2*1.5*√2x+1.5^2=(√2x-1.5)^2
2.5=2.25+0.25
√(2x^2-3√2x+2.5)==√[(√2x-1.5)^2+0.25]