解方程: x*(x+1)*(x+2)=504

2024-12-01 17:23:25
推荐回答(4个)
回答1:

x(x+1)(x+2)=504
x(x+1)(x+2)=7×8×9
x1=7 ,x^3+3x^2+2x-504=0, x^3-7x^2+10x^2-70x+72x-504=0
(x-7)(x^2+10x+72)=0 x1=7, x2=-5+i根号(47),x3==-5-ii根号(47),

回答2:

x*(x+1)*(x+2)=504
x(x^2+3x+2)-504=0
x^3+3x^2+2x-(7^3+3*7^2+2*7)=0
x^3-7^3+3x^2-3*7^2+2x-2*7=0
(x-7)(x^2+7x+49)+3(x-7)(x+7)+2(x-7)=0
(x-7)[(x^2+7x+49)+3(x+7)+2]=0
(x-7)(x^2+7x+49+3x+21+2)=0
(x-7)(x^2+10x+72)=0
(x-7)[(x^2+10x+25-25+72]=0
(x-7)[(x+5)^2+47]=0(因为(x+5)^2+47>0)
x-7=0
x=7

回答3:

x*(x+1)*(x+2)=504=7*8*9
x=7

回答4:

x(x+1)(x+2)=504
x(x+1)(x+2)=7×8×9
x=7