Question

解方程：(x-1)(x-2)(x-3)(x-4)=1×2×3×4

Answer 1

(x-1)(x-4)＝(x^2-5x)＋4 (x-2)(x-3)＝(x^2-5x)＋6 所以,(x-1)(x-2)(x-3))(x-4)＝(x^2-5x)^2＋10(x^2-5x)＋24 方程(x-1)(x-2)(x-3)(x-4)=1×2×3×4化为(x^2-5x)^2＋10(x^2-5x)＝0 得x^2－5x＝0或x^2－5x＋10＝0,解得x＝0或5 所以,方程有二0和5