Question

解方程X×(X+1)×(X+2)×(X+3)=360,

Answer 1

[x(x+3)][(x+1)(x+2)]=360

(x^2+3x)(x^2+3x+2)=360

设t=x^2+3x+1,则有(t-1)(t+1)=360,解得t^2=361,t1=19,t2=-19

则有x^2+3x+1=19,解得x1=3,x2=-6

或x^2+3x+1=-19,此时(x+3/2)^2+71/4=0,矛盾,舍去

所以x1=3,x2=-6