题目

解方程x^2+10(x-1)√x+14x+1=0

提问时间：2020-06-18

答案

x^2+10(x-1)√x+14x+1=0
令 √x=y
y^4+10y^3+14y^2-10y+1=0 (y>=0)
y^2+10y+14-10/y+1/y^2=0
(y-1/y)^2+10(y-1/y)+16=0
(y-1/y+2)(y-1/y+8)=0
(1) y-1/y=-2
y^2+2y-1=0
(y+1-√2）(y+1+√2）=0
则 y=√2-1,x=3-2√2
(2) y-1/y=-8
y^2+8y-1=0
(y+4-√17）(y+4+√17）=0
则 y=√17-1,x=18-2√17
【OK?】