Question

解方程6x^5-41x^4+97x^3-97x^2+41x-6=0

Answer 1

将原等式左边分解因式得如下过程：

6x^5-41x^4+97x^3-97x^2+41x-6

= (x-1)(6x^4-35x^3+62x^2-35x+6)

= (x-1)(x-2)(6x^3-23x^2+16x-3)

= (x-1)(x-2)(x-3)(6x^2-5x+1)

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

故得方程所有x=1,x=2,x=3,x=1/2,x=1/3,