x^4-23x^2+1分解因式,求详细步骤

2025-01-03 13:44:40
推荐回答(4个)
回答1:

x^4-23x^2+1
=x^4+2x^2+1-25x^2
=(x^2+1)^2-25x^2
=(x^2-5x+1)(x^2+5x+1)
这两个2次因式判别式小于0,在实数范围不能再分解。

回答2:

x^2-23x+1
=(x^2-23x+529/4)-525/4
=(x-23/2)^2-525/4
=(x-23/2+5√21/2)(X-23/2-5√21 /2)

回答3:

x^4-23x²+1
=x^4+2x²+1-25x²
=(x²+1)²-25x²
=(x²+1+5x)(x²+1-5x)

回答4:

x^4-2x^2+1=(x^2)^2-2x^2+1=(x^2-1)^2=[(x+1)(x-1)]^2