x(x+2)(x+3)(x+5)=7

来源：学生作业帮助网编辑：作业帮时间：2024/04/29 00:22:58

x(x+2)(x+3)(x+5)=7
x(x+2)(x+3)(x+5)=7

x(x+2)(x+3)(x+5)=7
x(x+2)(x+3)(x+5)=7
[x(x+5)][(x+2)(x+3)]=7
(x²+5x)(x²+5x+6)-7=0
(x²+5x)[(x²+5x)+6]-7=0
(x²+5x)²+6(x²+5x)-7=0
[(x²+5x)+7][(x²+5x)-1]=0
(x²+5x+7)(x²+5x-1)=0
x²+5x+7=0
∵△=5²-4×1×7=25-27=-3<0
∴方程无解
或
x²+5x-1=0
x={-5±√(5²-4×1×(-1))}/(2×1)
x=(-5±√29)/2
x1=(-5+√29)/2,x2=(-5-√29)/2
综上所述：x1=(-5+√29)/2,x2=(-5-√29)/2

x(x+2)(x+3)(x+5)=7
[x(x+5)][(x+2)(x+3)]-7=0
(x²+5x)(x²+5x+6)-7=0
(x²+5x)²+6(x²+5x)-7=0
(x²+5x-1)(x²+5x+7)=0
因为x²+5x+7=(x+5/2)²+3/4>0
所以x²+5x-1=0
所以x=(-5±√29)/2
望采纳

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