(9+4根号2)x^2-(1+2根号2)x-2=0解方程

(9+4√2)x²-(1+2√2)x-2=0
[(1+2√2)x]²-[2×(1+2√2)×(1/2)]x+(1/2)²-(1/2)²-2=0
[(1+2√2)x-1/2]²-(1/2)²-2=0
[(1+2√2)x-1/2]²=9/4
(1+2√2)x-1/2=±3/2
(1+2√2)x=(1±3)/2
x1=(1+3)/[2(1+2√2)]=2(1-2√2)/[(1+2√2)(1-2√2)]=(4√2-2)/7
x1=(1-3)/[2(1+2√2)]=-(1-2√2)/[(1+2√2)(1-2√2)]=(2√2-1)/7

(9+4根号2)x^2-(1+2根号2)x-2=0
[（1+2根号2）x]²-(1+2根号2)x-2=0
【（1+2根号2）x-2】【（1+2根号2）x+1】=0
x=2/（1+2根号2）或x=-1/（1+2根号2）