x3+根号3x2+(2根号3-1)x+3-根号3=0急,急,急,

Question

x3+根号3x2+(2根号3-1)x+3-根号3=0 急,急,急,

Answer 1

x³+√3·x²+(2√3-1)x+3-√3=0
x³+(√3-1)x²+x²+(2√3-1)x+3-√3=0
x²(x+√3-1)+[x²+(2√3-1)x+3-√3]=0
x √3
x √3-1
(√3-1)x+√3·x=(2√3-1)x
x²(x+√3-1)+(x+√3)(x+√3-1)=0
(x+√3-1)(x²+x+√3)=0
x+√3-1=0,或x²+x+√3=0
x1=1-√3,x2=[-1+√(1-4√3)]/2,x3=[-1-√(1-4√3)]/2
若在实属范围内求解,则只取x1=1-√3即可,后面两根为虚数舍去