Question

4x^2-6x-6-x根号(x^2-x-1)=0请写出详细过程

Answer 1

6x^2-6x-6-x√(x^2-x-1)-2x^2=0

6(√(x^2-x-1))^2-x√(x^2-x-1)-2x^2=0

[3√(x^2-x-1)-2x]*[2√(x^2-x-1)+x]=0,

2√(x^2-x-1)+x=0,没有实数解,

3√(x^2-x-1)-2x=0,

9(x^2-x-1)=4x^2,

5x^2-9x-9=0,

x=(9±3√29)/10.

经检验,去除负根,x=(9+3√29)/10是原方程的解.