x(x-1)(x+1)(x+2)=24 срочно решите. Created by Alli11111. algebra-ru

x(x-1)(x+1)(x+2)=24 срочно решите...

nafanya2014

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(x-1)·(x+2)·x·(x+1)=24;
(x²+x-2)·(x²+x)=24

x²+x=t
(t-2)·t=24
t²-2t-24=0
D=4+96=100
t=(2-10)/2=-4 или t=(1+10)/2=6

x²+x= - 4 или x²+x=6
x²+x+4=0 или x²+x-6=0
D=1-16<0 D=1+24=25
нет корней х=(-1-5)/2=-3 или х=(-1+5)/2=2
О т в е т. -3;2

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sangers1959

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X(x-1)(x+1)(x+2)=24
x(x-1)(x+1)(x+2)=2*1*3*4=24
x(x-1)(x+1)(x+2)=2*(2-1)*(2+1)*(2+2)=2*1*3*4=24 ⇒
x₁=2.
x(x-1)(x+1)(x+2)=(-1)*(-2)*(-3)*(-4)
x(x-1)(x+1)(x+2)=(-3)*(-3-1)*(-3+1)*(-3+2)=(-3)*(-4)*(-2)*(-1)=24 ⇒
x₂=-3.
Ответ: x₁=2 x₂=-3.

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