\(\left(x-4\right)\left(x-6\right)< 0\\ \Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-4< 0\\x-6>0\end{matrix}\right.\\\left\{{}\begin{matrix}x-4>0\\x-6< 0\end{matrix}\right.\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x< 4\\x>6\left(vô.lí\right)\end{matrix}\right.\\\left\{{}\begin{matrix}x>4\\x< 6\end{matrix}\right.\end{matrix}\right.\)

\(\Rightarrow4< x< 6\)

Mà x là số nguyên nên x=5

Để \(\left(x-4\right)\left(x-6\right)< 0\) thì \(\left(x-4\right)\) và \(\left(x-6\right)\) trái dấu

Hay \(x-4>0;x-6< 0\) => \(x>4;x< 6\Rightarrow x=\left\{5\right\}\)

hoặc \(x-4< 0;x-6>0\) => \(x< 4;x>6\Rightarrow x\in\varnothing\)

Vậy: Giá trị x nguyên thỏa mãn điều kiện là 5.

3x.(x-2)-x²+2x=0

⇔3x²-6x-x²+2x=0

⇔2x²-4x=0

⇔2x(x-2)=0

\(\Leftrightarrow\left[{}\begin{matrix}2x=0\\x-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=2\end{matrix}\right.\)

vậy x=0 và x=2

3x(x-2)-x^2+2x=0

<=>3x(x-2)-x(x-2)=0

<=>(3x-x)(x-2)=0

<=>2x(x-2)=0

<=>2x=0 hoặc x-2=0

<=>x=0 hoặc x=2

\(3x\left(x-2\right)-x^2+2x=0\Rightarrow3x\left(x-2\right)-x\left(x-2\right)=0\Rightarrow\left(x-2\right)\left(3x-x\right)=0\Rightarrow\left[{}\begin{matrix}x-2=0\\2x=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=2\\x=0\end{matrix}\right.\)

giúp em  bài với ạ,em cảm ơn, em đang vội ạ

\(a,=-15x^3+10x^4+20x^2\\ b,=2x^3+2x^2+4x-x^2-x-2=2x^3+x^2+3x-2\)

`2x-2/3=1/2`

`2x=1/2+2/3`

`2x=7/6`

`x=7/6:2=7/12`

\(2x-\dfrac{2}{3}=\dfrac{1}{2}\Leftrightarrow2x=\dfrac{2}{3}+\dfrac{1}{2}=\dfrac{7}{6}\Leftrightarrow x=\dfrac{7}{6}:2=\dfrac{7}{12}\)

2x - 2/3 = 1/2

2x = 1/2 + 2/3 = 7/6

x = 7/6 : 2 = 7/12

vậy x = 7/12

mn trả lời đi mà,mình tick cho

5,2÷1,3

\(B=\left|x-3\right|+\left|x-5\right|\)

Vì \(\left|x-3\right|,\left|x-5\right|\ge0\forall x\)

\(\Rightarrow\left|x-3\right|+\left|x-5\right|\ge0\forall x\)

\(\Rightarrow B\ge0\)

+) Nếu \(x< 3\Rightarrow\left|x-3\right|=3-x,\left|x-5\right|=5-x\) 

\(\Rightarrow B=\left|x-3\right|+\left|x-5\right|=3-x+5-x=8-2x\)

TH1: Nếu \(x< 0\Rightarrow-x>0\Rightarrow B=8+2\left(-x\right)>8\)

TH2: Nếu \(x=0\Rightarrow B=8\)

TH3: Nếu \(0< x< 3\Rightarrow B=8-2x< 8\)

+) Nếu \(x=3\Rightarrow\left|x-3\right|=0,\left|x-5\right|=2\) 

\(\Rightarrow B=\left|x-3\right|+\left|x-5\right|=2\)

+) Nếu \(3< x< 5\Rightarrow\left|x-3\right|=x-3,\left|x-5\right|=5-x\) 

\(\Rightarrow B=\left|x-3\right|+\left|x-5\right|=x-3+5-x=2\)

+) Nếu \(x=5\Rightarrow\left|x-3\right|=2,\left|x-5\right|=0\)

\(\Rightarrow B=\left|x-3\right|+\left|x-5\right|=2\)

+) Nếu \(x>5\Rightarrow\left|x-3\right|=x-3,\left|x-5\right|=x-5\)

\(B=\left|x-3\right|+\left|x-5\right|=x-3+x-5=2x-8>2\)

\(\Rightarrow B_{max}>8\Leftrightarrow x< 0\)