解方程:(x-1)(x-2)(x+2)(x+3)=60

解方程:(x-1)(x-2)(x+2)(x+3)=60
[(x-1)(x+2)][(x-2)(x+3)]=(x²+x-2)(x²+x-6)=(x²+x)²-8(x²+x)+12=60
即有(x²+x)²-8(x²+x)-48=(x²+x-12)(x²+x+4)=0
由x²+x-12=(x+4)(x-3)=0，得x₁=-4；x₂=3；
由x²+x+4=0，得x₃=(-1+i√15)/2；x₄=(-1+i√15)/2；

解方程:
(x-1)(x-2)(x+2)(x+3)=60
(x^2-4)(x-1)(x+3)=5*2*6
那么：x^2-4=5
x1=3 x2=-3 (不合题意，舍去）
x-1=2
x3=3
x+3=6
x4=3
即：x=3

数学之美团为你解答(x-1)(x-2)(x+2)(x+3)=60[(x-1)(x+2)] [(x-2)(x+3)] = 60(x²+x-2)(x²+x-6)=60(x²+x)²-8(x²+x)+12=60(x²+x)²-8(x²+x)-48=0(x²+x-12)(x²+x+4)=0...