(x-1)(x-2)(x-3)(x-4)+1=0

来源：百度知道编辑：UC知道时间：2024/05/30 11:25:41

方程求解

(x-1)(x-2)(x-3)(x-4)+1
=(x*x-5x)平方+10(x*x-5x)+24+1
=(x*x-5x)平方+10(x*x-5x)+25
=(x*x-5x+5)平方

所以有:(X^2-5X+5)^2=0

X^2-5X+5=0

(X-5/2)^2=5/4

X1=5/2+根5/2

X2=5/2-根5/2

(x-1)(x-2)(x-3)(x-4)+1=0
(x-1)(x-4)(x-2)(x-3)+1=0
(x^2-5x+4)(x^2-5x+6)+1=0
(x^2-5x+4)(x^2-5x+4+2)+1=0
[(x^2-5x+4)^2+2*(x^2-5x+4)+1=0

(x^2-5x+4+1)^2=0

[x^2-5x+(5/2)^2+5-(5/2)^2]^2=0
[(x-5/2)^2+(20-25)/4]^2=0
[(x-5/2)^2-5/4]^2=0

(x-5/2)=±(√5)/2

x=5/2±(√5)/2

x=[5±(√5)]/2

[(x-1)(x-4)][(x-2)(x-3)]+1=0

[(x^2-5x+5)-1][(x^2-5x+5)+1]+1=0

(x^2-5x+5)^2-1^2+1=0

x^2-5x+5=0

后面就easy了吧

1+x+x^2+x^3=0 ,求x+x^2+x^3+...+x^2000 分解公因式(1+X)+X(1+X)+X(1+X)^2+X(1+X)^3+...+X(1+X)^99 X*X-2X-1＝0 求2x*x*x-3*x*x-4*x+2 (x-1) (x平方-3X+2) 解方程(x+1)(x+2)(x+3)(x+4)=(x+1)(x+1)+(x+2)(x+2)+(x+3)(x+3)+(x+4)(x+4) (x+1)(x+2)(x+3)(x+4)=(x+1)(x+1)+(x+2)(x+2)+(x+3)(x+3)+(x+4)(x+4) (X^2-X+1)^2-3(X^2-X)-7 数学题X(X+1)(X+2)(X+3)+1 因式分解(X+1)(X+2)(X+3)(X+4)+1 x(x-1)(x+2)(x+3)+1