解方程：x-6X-6-x根号x-2x-2=0x-2x-2在根号里面,解方程,要详解

Question

解方程：x-6X-6-x根号x-2x-2=0
x-2x-2在根号里面,解方程,要详解

Answer 1

x-6X-6-x根号x-2x-2=0 根号x-2x-2=(x-6X-6)/x=(x-6-6/x) 两边平方得 x-2x-2=(x-6)^2-12(x-6)/x+36/x^2 x-2x-2=x^2-12x+(36-12)+72/x+36/x^2 10x-26=72/x+36/x^2 5x-13=36/x+18/x^2 5x^3-13x^2=36x+18 5x^3-13x^2-36x-18=0 5x^3+5x^2-18x^2-36x-18=0 5x^2(x+1)-18(x^2+2x+1)=0 5x^2(x+1)-18(x+1)^2=0 (x+1)(5x^2-18x-18)=0 x+1=0或者5x^2-18x-18=0 x=-1 Δ=18x18+4x5x18=684=36x19 x=(18±6√19)/10 x=(9±3√19)/5 x-2x-2≥0 Δ=4+8=12 x≥1+√3 x≤ 1-√3 所以x=-1 x=(9±3√19)/5