Question

x的n次方加1怎么分解

Answer 1

n=3时,可以用公式：x^3+1=(x+1)(x^2-x+1)

n=4时,x^4+1=[x^2+(√2)x+1] [x^2-(√2)x+1]

n=5时,n^5+1=(x+1)(x^4-x^3+x^2-x+1)

n=6时,x^6+1=(x^2+1)[x^2+(√3)x+1][x^2-(√3)x+1]

n=7时,x^7+1=(x+1)(x^6-x^5+x^4-x^3+x^2-x+1)

你为奇数时简单

x^n+1=(x+1)(x^(n-1)-x^(n-2)+……x^3+x^2-x+1)

偶数时很麻烦