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15问答网 > 解方程：x（x+1）（x+2）（x+3）=120

解方程：x（x+1）（x+2）（x+3）=120

解方程：x（x+1）（x+2）（x+3）=120．

2025-03-15 00:59:04

推荐回答（1个）

回答1：

∵（x+1）（x+2）（x+3）（x+4）-120=0，
∵（x²+5x+6）（x²+5x+4）-120=0
∴（x²+5x）²+10（x²+5x）-96=0．
设x²+5x=t，则
t²+10t-96=0，
即（t+16）（t-5）=0．
解得 t=-16或t=5．
①当t=-16时，x²+5x=-16，即x²+5x+16=0．
∵△=25-64=-39＜0，
∴该方程无解；
②当t=6时，x²+5x=6，即
（x+6）（x-1）=0，
解得 x₁=-6，x₂=1．
综上所述，原方程的解是x₁=-6，x₂=1．

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