解方程:根号2x^3+4x^2+2根号2x+2-根号2=0

问题描述:

解方程:根号2x^3+4x^2+2根号2x+2-根号2=0

x^3+2√2x^2+2x+√2-1=0
x^3+(√2-1)x^2+(√2+1)x^2+x+x+√2-1=0
(x+√2-1)[x^2+(√2+1)x+1]=0
x1=1-√2
x2=[-√2-1+√(2√2-1)]/2
x3=[-√2-1-√(2√2-1)]/2

这个清楚