Question

(x+1)(x-1)(x²-x+1)(x²+x+1)计算 大根号 9-4根号5 化简 2x²+4x-3 分解因式

Answer 1

(x+1)(x-1)(x²-x+1)(x²+x+1)
=(x+1)(x²-x+1)((x-1)(x²+x+1)
=(x^3+1)(x^3-1)
=x^6-1
√（9-4√5）
=√（2-√5）^2
=√5-2
2x²+4x-3
=2(x²+2x+1)-2-3
=2(x+1)²-5
=2[(x+1)²-(√10/2)²]
=2(x+1+√10/2)(x+1-√10/2)

Answer 2

(x+1)(x-1)(x²-x+1)(x²+x+1)=[(x+1)(x²-x+1)][(x-1)(x²+x+1)]=x^6-1
大根号 9-4根号5 =大根号(根号5-2)的平方=根号5-2
2x²+4x-3=0的方程2根，用公式法，x1=-1+√10/2,x2=-1-√10/2
2x²+4x-3=2(x+1+√10/2)(x+1-√10/2)

Answer 3

(x+1)(x-1)(x²-x+1)(x²+x+1)=(x³+1)(x³-1)=x^6-1
√[9-4√5]=√(√5-2)^2=√5-2
2x²+4x-3 =2(x+1)^2-5= [√2(x+1)-√5] [√2(x+1)+√5]

Answer 4

x^6-1
根号5-2
无法分解