(x-2) x (3-x) = 0
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VM
25 tháng 10 2019
\(2x^2-6x=0\)
\(\Rightarrow2x.\left(x-3\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}2x=0\\x-3=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0:2\\x=0+3\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=3\end{matrix}\right.\)
Vậy \(x\in\left\{0;3\right\}.\)
\(2x.\left(x+2\right)-3.\left(x+2\right)=0\)
\(\Rightarrow\left(x+2\right).\left(2x-3\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x+2=0\\2x-3=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0-2\\2x=3\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-2\\x=3:2\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-2\\x=\frac{3}{2}\end{matrix}\right.\)
Vậy \(x\in\left\{-2;\frac{3}{2}\right\}.\)
\(x^3-16x=0\)
\(\Rightarrow x.\left(x^2-16\right)=0\)
\(\Rightarrow x.\left(x^2-4^2\right)=0\)
\(\Rightarrow x.\left(x-4\right).\left(x+4\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x-4=0\\x+4=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=0+4\\x=0-4\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=4\\x=-4\end{matrix}\right.\)
Vậy \(x\in\left\{0;4;-4\right\}.\)
Chúc bạn học tốt!
KV
9 tháng 1 2024
1) Do x ∈ Z và 0 < x < 3
⇒ x ∈ {1; 2}
2) Do x ∈ Z và 0 < x ≤ 3
⇒ x ∈ {1; 2; 3}
3) Do x ∈ Z và -1 < x ≤ 4
⇒ x ∈ {0; 1; 2; 3; 4}
TA
1
10 tháng 8 2017
\(\left(x-3\right)^3+\left(x+3\right)^3=0\)
\(\Leftrightarrow x^3-9x^2+27x-27+x^3+9x^2+27x+27=0\)\(\Leftrightarrow2x^3+54x^2=0\)
\(\Leftrightarrow x^2\left(2x+54\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\2x+54=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=-27\end{matrix}\right.\)
\(b,\left(x+1\right)^3-\left(x-1\right)^3=0\)
\(\Leftrightarrow x^3+3x^2+3x+1-x^3+3x^2-3x+1=0\)\(\Leftrightarrow6x^2+2=0\)
\(\Leftrightarrow6x^2=-2\)
\(\Leftrightarrow x^2=-3\) ( vô lí)
Vậy pt vô nghiệm
\(c,x^2-4x+3=0\)
\(\Leftrightarrow x^2-3x-x+3=0\)
\(\Leftrightarrow x\left(x-3\right)-\left(x-3\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x-3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\x-3=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=1\\x=3\end{matrix}\right.\)
\(d,4x^2+4x+1=0\)
\(\Leftrightarrow\left(2x+1\right)^2=0\)
\(\Rightarrow2x+1=0\)
\(\Leftrightarrow2x=-1\Rightarrow x=-\dfrac{1}{2}\)
\(e,\left(x+2\right)^2-\left(x+3\right)^2=0\)
\(\Leftrightarrow\left(x+2-x-3\right)\left(x+2+x+3\right)=0\)
\(\Leftrightarrow-\left(2x+5\right)=0\)
\(\Leftrightarrow-2x-5=0\)
\(\Leftrightarrow-2x=5\Rightarrow x=-\dfrac{5}{2}\)
Học tốt nha you <3
TA
1
10 tháng 8 2017
\(\left(x-3\right)^3+\left(x+3\right)^3=0\)
\(\Leftrightarrow x^3-9x^2+27x-27+x^3+9x^2+27x+27=0\)\(\Leftrightarrow2x^3+54x^2=0\)
\(\Leftrightarrow x^2\left(2x+54\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\2x+54=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=-27\end{matrix}\right.\)
\(b,\left(x+1\right)^3-\left(x-1\right)^3=0\)
\(\Leftrightarrow x^3+3x^2+3x+1-x^3+3x^2-3x+1=0\)\(\Leftrightarrow6x^2+2=0\)
\(\Leftrightarrow6x^2=-2\)
\(\Leftrightarrow x^2=-3\) ( vô lí)
Vậy pt vô nghiệm
\(c,x^2-4x+3=0\)
\(\Leftrightarrow x^2-3x-x+3=0\)
\(\Leftrightarrow x\left(x-3\right)-\left(x-3\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x-3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\x-3=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=1\\x=3\end{matrix}\right.\)
\(d,4x^2+4x+1=0\)
\(\Leftrightarrow\left(2x+1\right)^2=0\)
\(\Rightarrow2x+1=0\)
\(\Leftrightarrow2x=-1\Rightarrow x=-\dfrac{1}{2}\)
\(e,\left(x+2\right)^2-\left(x+3\right)^2=0\)
\(\Leftrightarrow\left(x+2-x-3\right)\left(x+2+x+3\right)=0\)
\(\Leftrightarrow-\left(2x+5\right)=0\)
\(\Leftrightarrow-2x-5=0\)
\(\Leftrightarrow-2x=5\Rightarrow x=-\dfrac{5}{2}\)
Học tốt nha you <3
TA
1
10 tháng 8 2017
\(\left(x-3\right)^3+\left(x+3\right)^3=0\)
\(\Leftrightarrow x^3-9x^2+27x-27+x^3+9x^2+27x+27=0\)\(\Leftrightarrow2x^3+54x^2=0\)
\(\Leftrightarrow x^2\left(2x+54\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\2x+54=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=-27\end{matrix}\right.\)
\(b,\left(x+1\right)^3-\left(x-1\right)^3=0\)
\(\Leftrightarrow x^3+3x^2+3x+1-x^3+3x^2-3x+1=0\)\(\Leftrightarrow6x^2+2=0\)
\(\Leftrightarrow6x^2=-2\)
\(\Leftrightarrow x^2=-3\) ( vô lí)
Vậy pt vô nghiệm
\(c,x^2-4x+3=0\)
\(\Leftrightarrow x^2-3x-x+3=0\)
\(\Leftrightarrow x\left(x-3\right)-\left(x-3\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x-3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\x-3=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=1\\x=3\end{matrix}\right.\)
\(d,4x^2+4x+1=0\)
\(\Leftrightarrow\left(2x+1\right)^2=0\)
\(\Rightarrow2x+1=0\)
\(\Leftrightarrow2x=-1\Rightarrow x=-\dfrac{1}{2}\)
\(e,\left(x+2\right)^2-\left(x+3\right)^2=0\)
\(\Leftrightarrow\left(x+2-x-3\right)\left(x+2+x+3\right)=0\)
\(\Leftrightarrow-\left(2x+5\right)=0\)
\(\Leftrightarrow-2x-5=0\)
\(\Leftrightarrow-2x=5\Rightarrow x=-\dfrac{5}{2}\)
Học tốt nha you <3
DL
5
NK
8 tháng 2 2016
Làm theo công thức: tích bằng 0 thì một trong x thừa số bằng 0 rồi xét các trường hợp
1 tháng 2 2017
\(1,x.\left(x+7\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\\x+7=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=0\\x=-7\end{cases}}}\)
\(2,\left(x+12\right).\left(x-3\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x+12=0\\x-3=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=-12\\x=3\end{cases}}}\)
\(3,\left(-x+5\right).\left(3-x\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}-x+5=0\\3-x=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=5\\x=3\end{cases}}}\)
2 tháng 2 2021
4/ \(x.\left(2+x\right).\left(7-x\right)=0\)
\(\hept{\begin{cases}x=0\\2+x=0\\7-x=0\end{cases}}\) => \(\hept{\begin{cases}x=0\\x=-2\\x=7\end{cases}}\)
Vậy \(x=\left\{0,-2,7\right\}\)
5/ \(\left(x-1\right).\left(x+2\right).\left(-x-3\right)=0\)
\(\hept{\begin{cases}x-1=0\\x+2=0\\-x-3=0\end{cases}}\)=> \(\hept{\begin{cases}x=1\\x=-2\\x=-3\end{cases}}\)
TT
Tìm x biết:
a) x^2-3.x=0
b) 2.x^2+5.x=0
c) x^2+1=0
d) x^2-1=0
e) x.(x-3)-x+3=0
g) x^2.(x+2)-9.x-18=0
1
LN
31 tháng 12 2017
a)x^2-3.x=0
x^3.(1-3)=0
x^3.(-2)=0
x^3=0:(-2)
x^3=0
x=0
b)2.x^2+5.x=0
x^3.(2+5)=0
x^3.7=0
x^3=0:7
x^3=0
x=0
c)x^2+1=0
x^2=0-1
x^2=(-1)
x ko thỏa mãn
d)x^2-1=0
x^2=0+1
x^2=1
x=1 hoặc x=(-1)
e)x.(x-3)-x+3=0
Mình ko bt xin lỗi
g)x^2.(x+2)-9.x-18=0
x^2.(x+2)-9.x=0+18
x^2.(x+2)-9.x=18
x^2.x+x^2.2-9.x=18
Mk chỉ giải đc đến đây thôi. Xin lỗi!
TT
5
TD
5 tháng 2 2017
1/ ( x+12)(3-x)=0
=> \(\orbr{\begin{cases}x+12=0\\3-x=0\end{cases}}\)
=>\(\orbr{\begin{cases}x=-12\\x=3\end{cases}}\)
( x - 2 )( 3 - x ) = 0
⇒ x - 2 = 0 hoặc 3 - x = 0
Nếu x - 2 = 0 ⇒ x = 0 + 2 = 2
Nếu 3 - x = 0 ⇒ x = 3 - 0 = 3
Vậy x ϵ { 2; 3 } để ( x - 2 )( 3 - x ) = 0
`(x-2)(3-x)=0`
`=> [(x-2=0),(3-x=0):}`
`=> [(x=2),(x=3):}`
Vậy `xin{2;3}`