解方程：x^2-6x-6-x√x^2-2x-2=0

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/04/29 19:28:33

解方程：x^2-6x-6-x√x^2-2x-2=0
根号下是x^2-2x-2

x^2-6x-6=x√(x^2-2x-2)
两边平方
x^4+36x^2+36-12x^3-12x^2+72x=x^4-2x^3-2x^2
5x^3-13x^2-36x-18=0
5x^3+5x^2-18x^2-36x-18=0
5x^2(x+1)-18(x+1)^2=0
(x+1)(5x^2-18x-18)=0
x=-1,x=(9±3√19)/5
经检验x=(9+3√19)/5是增根
所以x1=-1,x2=(9-3√19)/5

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