解方程（x²+3x+2)(x²-2x-1)(x²-7x+12)+24=0

解方程（x²+3x+2)(x²-2x-1)(x²-7x+12)+24=0
解方程（x²+3x+2)(x²-2x-1)(x²-7x+12)+24=0

解方程（x²+3x+2)(x²-2x-1)(x²-7x+12)+24=0
(x+1)(x+2)(x^2-2x-1)(x-3)(x-4)+24=0
(x+1)(x-3)(x+2)(x-4)(x^2-2x-1)+24=0
(x^2-2x-3)(x^2-2x-8)(x^2-2x-1)+24=0,记x^2-2x=t
(t-3)(t-8)(t-1)+24=0
t^3-12t^2+35t=0
t(t-5)(t-7)=0
t=0--> x^2-2x=0--> x=0,2
t=5--> x^2-2x=5-->x=1+√6,1-√6
t=7-->x^2-2x=7-->x=1+2√2,1-2√2.
因此共有上面6个解.

用观察法 看出X=0