作业帮求根号[（x+1）²）+36]-根号[（x-2）²+4]的最大值是____
来源：学生作业帮助网 编辑：作业帮 时间：2024/04/27 14:14:55
![求根号[（x+1）²）+36]-根号[（x-2）²+4]的最大值是____](/uploads/image/z/15253275-3-5.jpg?t=%E6%B1%82%E6%A0%B9%E5%8F%B7%5B%EF%BC%88x%2B1%EF%BC%89%26sup2%3B%EF%BC%89%2B36%5D-%E6%A0%B9%E5%8F%B7%5B%EF%BC%88x-2%EF%BC%89%26sup2%3B%2B4%5D%E7%9A%84%E6%9C%80%E5%A4%A7%E5%80%BC%E6%98%AF____)
求根号[（x+1）²）+36]-根号[（x-2）²+4]的最大值是____
求根号[（x+1）²）+36]-根号[（x-2）²+4]的最大值是____
求根号[（x+1）²）+36]-根号[（x-2）²+4]的最大值是____
设：Y=((x+1)^2+36)^0.5-((x-2)^2+4)^0.5
Y'=(1/2)*2*(x+1)((x+1)^2+36)^(-0.5)-(1/2)*2*(x-2)((x-2)^2+4)^(-0.5)=0
(x+1)/((x+1)^2+36)^0.5-(x-2)/((x-2)^2+4)^0.5=0
(x+1)/((x+1)^2+36)^0.5=(x-2)/((x-2)^2+4)^0.5
(x+1)^2/((x+1)^2+36)=(x-2)^2/((x-2)^2+4)
1/(1+36/(x+1)^2)=1/(1+4/(x-2)^2)
1+36/(x+1)^2=1+4/(x-2)^2
36/(x+1)^2=4/(x-2)^2
36*(x-2)^2=4*(x+1)^2
9*(x-2)^2=(x+1)^2
9x^2-36x+36=x^2+2x+1
8x^2-38x+35=0
x1=(38+(38^2-4*8*35)^0.5)/16=(38+(324)^0.5)/16=(38+18)/16=3.5
x2=(38-(38^2-4*8*35)^0.5)/16=(38-(324)^0.5)/16=(38-18)/16=1.25
Y1=((x+1)^2+36)^0.5-((x-2)^2+4)^0.5=(4.5^2+36)^0.5-(1.5^2+4)^0.5=5
Y2=((x+1)^2+36)^0.5-((x-2)^2+4)^0.5=(2.25^2+36)^0.5-((-0.75)^2+4)^0.5=4.272
最大值是Y1=5