\(a,\dfrac{x-3}{x}=\dfrac{x-3}{x+3}\)\(\left(đk:x\ne0,-3\right)\)

\(\Leftrightarrow\dfrac{x-3}{x}-\dfrac{x-3}{x+3}=0\)

\(\Leftrightarrow\dfrac{\left(x-3\right)\left(x+3\right)-x\left(x-3\right)}{x\left(x+3\right)}=0\)

\(\Leftrightarrow x^2-9-x^2+3x=0\)

\(\Leftrightarrow3x-9=0\)

\(\Leftrightarrow3x=9\)

\(\Leftrightarrow x=3\left(n\right)\)

Vậy \(S=\left\{3\right\}\)

\(b,\dfrac{4x-3}{4}>\dfrac{3x-5}{3}-\dfrac{2x-7}{12}\)

\(\Leftrightarrow\dfrac{4x-3}{4}-\dfrac{3x-5}{3}+\dfrac{2x-7}{12}>0\)

\(\Leftrightarrow\dfrac{3\left(4x-3\right)-4\left(3x-5\right)+2x-7}{12}>0\)

\(\Leftrightarrow12x-9-12x+20+2x-7>0\)

\(\Leftrightarrow2x+4>0\)

\(\Leftrightarrow2x>-4\)

\(\Leftrightarrow x>-2\)

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

`<=>3+(x^2-3x-3)(x^2-3x+3)=0`

`<=>3+(x^2-3x)^2-9=0`

`<=>(x^2-3x)^2-6=0`

`<=>x^2-3x=+-6`

Đến đây chia 2 th rồi giải thôi :v

1) \(\sqrt[]{3x+7}-5< 0\)

\(\Leftrightarrow\sqrt[]{3x+7}< 5\)

\(\Leftrightarrow3x+7\ge0\cap3x+7< 25\)

\(\Leftrightarrow x\ge-\dfrac{7}{3}\cap x< 6\)

\(\Leftrightarrow-\dfrac{7}{3}\le x< 6\)

\(\dfrac{3x}{x^2-x+3}-\dfrac{2x}{x^2-3x+3}+1=0\left(a\right)\)

Ta có : \(x^2-x+3=x^2-x+\dfrac{1}{4}+\dfrac{11}{4}=\left(x-\dfrac{1}{2}\right)^2+\dfrac{11}{4}>0\)

\(x^2-3x+3=x^2-3x+\dfrac{9}{4}+\dfrac{3}{4}=\left(x-\dfrac{3}{2}\right)^2+\dfrac{3}{4}>0\)

\(\RightarrowĐKXĐ:x\in R\)

Đặt : \(t=x^2-x+3\)

\(\left(a\right)\Leftrightarrow\dfrac{3x}{t}-\dfrac{2x}{t-2x}+1=0\)

\(\Leftrightarrow3x\left(t-2x\right)-2xt+t\left(t-2x\right)=0\)

\(\Leftrightarrow t^2-xt-6x^2=0\)

\(\Leftrightarrow t^2+2xt-3xt-6x^2=0\)

\(\Leftrightarrow t\left(t+2x\right)-3x\left(t+2x\right)=0\)

\(\Leftrightarrow\left(t-3x\right)\left(t+2x\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}t-3x=0\\t+2x=0\end{matrix}\right.\left(b\right)\)

Thay ​\(t=x^2-x+3\) ​lại vào (b) được :

\(\left[{}\begin{matrix}x^2-x+3-3x=0\\x^2-x+3+2x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x^2-4x+3=0\\x^2+x+3=0\end{matrix}\right.\left(c\right)\)

Mà : \(x^2-4x+3=x^2-x-3x+3\)

\(=x\left(x-1\right)-3\left(x-1\right)=\left(x-1\right)\left(x-3\right)\left(c'\right)\)

và : \(x^2+x+3=x^2+x+\dfrac{1}{4}+\dfrac{11}{4}\)

\(=\left(x+\dfrac{1}{2}\right)^2+\dfrac{11}{4}\left(c''\right)\)

Thay (c') và (c'') vào (c) được :

\(\left[{}\begin{matrix}\left(x-1\right)\left(x-3\right)=0\\\left(x+\dfrac{1}{2}\right)^2+\dfrac{11}{4}=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\left[{}\begin{matrix}x-1=0\Leftrightarrow x=1\left(tmđk\right)\\x-3=0\Leftrightarrow x=3\left(tmđk\right)\end{matrix}\right.\\\left(x+\dfrac{1}{2}\right)^2=-\dfrac{11}{4}\Leftrightarrow x\in\varnothing\end{matrix}\right.\)

Vậy : Phương trình có tập nghiệm \(S=\left\{1;3\right\}\)

a) \(x^3-3x^2-4x=0\)

\(\Leftrightarrow x\left(x^2-3x-4\right)=0\)

\(\Leftrightarrow x\left(x-4\right)\left(x+1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x-4=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=4\\x=-1\end{matrix}\right.\)

Vậy \(S=\left\{0;4;-1\right\}\).

b) \(3x^2-5x-2=0\)

\(\Leftrightarrow3x^2+x-6x-2=0\)

\(\Leftrightarrow x\left(3x+1\right)-2\left(3x+1\right)=0\)

\(\Leftrightarrow\left(3x+1\right)\left(x-2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}3x+1=0\\x-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{1}{3}\\x=2\end{matrix}\right.\)

Vậy \(S=\left\{-\dfrac{1}{3};2\right\}\).

Với câu a)bạn nhân cả 2 vế cho 12 rồi ép vào dạng bình phương 3 số

Câu b)bạn nhân cho 8 mỗi vế rồi ép vào bình phương 3 số 

giải zõ hộ

\(a,f'\left(x\right)=3x^2-6x\\ f'\left(x\right)\le0\Leftrightarrow3x^2-6x\le0\\ \Leftrightarrow3x\left(x-2\right)\le0\Leftrightarrow0\le x\le2\)

Lời giải:

a. $f'(x)\leq 0$

$\Leftrightarrow 3x^2-6x\leq 0$

$\Leftrightarrow x(x-2)\leq 0$

$\Leftrightarrow 0\leq x\leq 2$

b.

$f'(x)=x^2-3x+2=0$

$\Leftrightarrow 3x^2-6x=x^2-3x+2=0$

$\Leftrightarrow 3x(x-2)=(x-1)(x-2)=0$

$\Leftrightarrow x-2=0$

$\Leftrightarrow x=2$

c.

$g(x)=f(1-2x)+x^2-x+2022$

$g'(x)=(1-2x)'f(1-2x)'_{1-2x}+2x-1$

$=-2[3(1-2x)^2-6(1-2x)]+2x-1$
$=-24x^2+2x+5$

$g'(x)\geq 0$

$\Leftrightarrow -24x^2+2x+5\geq 0$

$\Leftrightarrow (5-12x)(2x-1)\geq 0$

$\Leftrightarrow \frac{-5}{12}\leq x\leq \frac{1}{2}$

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

\(\Delta=b^2-4ac=\left(-3\right)^2-4.1.2=1\)

=> pt có 2 nghiệm pb

\(x_1=\frac{-\left(-3\right)+1}{2}=2\)

\(x_2=\frac{-\left(-3\right)-1}{2}=1\)

a) Dễ thấy phương trình có a + b + c = 0 

nên pt đã cho có hai nghiệm phân biệt x₁ = 1 ; x₂ = c/a = 2

b) \(\hept{\begin{cases}x+3y=3\left(I\right)\\4x-3y=-18\left(II\right)\end{cases}}\)

Lấy (I) + (II) theo vế => 5x = -15 <=> x = -3

Thay x = -3 vào (I) => -3 + 3y = 3 => y = 2

Vậy pt có nghiệm ( x ; y ) = ( -3 ; 2 )

a, x1 = 1 , x2 = 2

b, x = -3 , y = 2

c, A = 1

d, x = -1 , x= 3