Question

若X²-X-2=0求X²-X+2√3/（X²-X）²-1+√3

若X²-X-2=0求X²-X+2√3
-------------- 的值
（X²-X）²-1+√3

Answer 1

X²-X-2=0
(x-2)(x+1)=0 x1=2 x2=-1
将x1=2代入上式
[X²-X+2√3]/[（X²-X）²-1+√3]=[2²-2+2√3]/[（2²-2）²-1+√3]=[2+2√3]/[3+√3]
=[(2+2√3)(3-√3）]/[(3+√3)(3-√3）]=(6+4√3-6)/6=2√3/3

将x2=-1代入上式
[X²-X+2√3]/[（X²-X）²-1+√3]=[(-1)²-(-1)+2√3]/[（(-1)²-(-1)）²-1+√3]=[2+2√3]/[3+√3]
=[(2+2√3)(3-√3）]/[(3+√3)(3-√3）]=(6+4√3-6)/6=2√3/3

X²-X-2=0→X²-X=2代入上式

[X²-X+2√3]/[（X²-X）²-1+√3]=[2+2√3]/[2²-1+√3]=[2+2√3]/[3+√3]
=[(2+2√3)(3-√3）]/[(3+√3)(3-√3）]=(6+4√3-6)/6=2√3/3

Answer 2

Answer 3

X²-X-2=0
X²-X=2
X²-X+2√3 2+2√3
-------------- =_________ =（3分之2）根号3
（X²-X）²-1+√3 4-1+√3