Tìm x[Toán 8]

P

passivedefender

[tex]x(x+1)(x+2)(x+3)-24=0[/tex]
[tex](x^{2}+3x)(x^{2}+3x+2)-24=0[/tex]
[tex](x^{2}+3x+1)^{2}-1-24=0[/tex]
[tex](x^{2}+3x+1)^{2}=25[/tex]
[tex]\Rightarrow x^{2}+3x+1= \pm 5[/tex]
*[tex]x^{2}+3x+1=5[/tex]
[tex]x^{2}+4x-x-4=0[/tex]
[tex]x(x+4)-(x+4)=0[/tex]
[tex](x+4)(x-1)=0[/tex]
[tex]x=-4[/tex] ; [tex]x=1[/tex] (1)
*[tex]x^{2}+3x+1=-5[/tex]
[tex]x^{2}+3x+6=0[/tex]
[tex]x^{2}+3x+\frac{9}{4}=-\frac{15}{4}[/tex]
[tex](x+\frac{3}{2})^{2} \geq 0[/tex]
[tex]\Rightarrow (x+\frac{3}{2})^{2}=-\frac{15}{4}<0[/tex] (tào lao) (2)
[tex](1),(2) \Rightarrow x=-4[/tex] ; [tex]x=1[/tex]
 
C

chipcoi_no.love

Tìm x, biết: x(x+1)(x+2)(x+3)-24=0

\Leftrightarrow[tex][x(x+3)][(x+1)(x+2)]-24=0[/tex]

\Leftrightarrow[tex](x^2+3x)(x^2+3x+2)]-24=0[/tex]

\Leftrightarrow[tex](x^2+3x+1-1)(x^2+3x+1+1)-24=0[/tex]

\Leftrightarrow[tex](x^2+3x+1)^2-1^2-24=0[/tex]

\Leftrightarrow[tex](x^2+3x+1)^2-5^2=0[/tex]

\Leftrightarrow[tex](x^2+3x+1+5)(x^2+3x+1-5)=0[/tex]

\Leftrightarrow[tex]x^2+3x+6=0[/tex] hoặc [tex]x^2+3x-4=0[/tex]

Vì [tex] x^2+3x+6 > 0 [/tex] \forall x thuộc R

\Rightarrowx(x+1)(x+2)(x+3)-24=0

\Leftrightarrow[tex]x^2+3x-4=0[/tex]

\Leftrightarrow[tex](x-1)(x+4)=0[/tex]

\Leftrightarrow x=1 hoặc x=-4
 
C

chipcoi_no.love

Tìm n thuộc Z sao cho: [tex](2n^2-n+2)[/tex] chia hết cho (2n+1)

[tex]2n^2-n+2[/tex]

[tex]=(2n^2+n)-(2n+1)+3[/tex]

[tex](2n^2-n+2)[/tex] chia hết cho (2n+1)

\Leftrightarrow [tex](2n^2+n)-(2n+1)+3[/tex] chia hết cho 2n+1

\Leftrightarrow 2n+1 là ước của 3

\Rightarrow 2n+1 = 3

\Leftrightarrow 2n = 2

\Leftrightarrow n = 1

Hoặc 2n+1 = -3

\Leftrightarrow 2n = -4

\Leftrightarrow n = -2

Hoặc 2n+1 = 1

\Leftrightarrow 2n = 0

\Leftrightarrow n = 0

Hoặc 2n+1 = -1

\Leftrightarrow 2n = -2

\Leftrightarrow n = -1
 
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