\(\left(3x+1\right)\left(x-3\right)=\left(3x+1\right)\left(2x-5\right)\)

\(\Leftrightarrow\left(3x+1\right)\left(x-3\right)-\left(3x+1\right)\left(2x-5\right)=0\)

\(\Leftrightarrow\left(3x+1\right)\left(x-3-2x+5\right)=0\)

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

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

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

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

Vậy tập nghiệm của pt là \(S=\left\{-\frac{1}{3};2\right\}\)

Có : \(\left(3x+1\right)\left(x-3\right)=\left(3x+1\right)\left(2x-5\right)\)

\(\Leftrightarrow\) \(\left(3x+1\right)\left(x-3\right)-\left(3x+1\right)\left(2x-5\right)=0\)

\(\Leftrightarrow\) \(\left(3x+1\right)\left(x-3-2x+5\right)=0\)

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

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

Vậy phương trình có tập nghiệm \(S=\left\{\frac{-1}{3};2\right\}\)

\(\left(x-3\right)-\frac{\left(x-3\right)\left(2x-5\right)}{6}=\frac{\left(x-3\right)\left(3-x\right)}{4}\)

\(\Leftrightarrow\frac{24\left(x-3\right)}{24}-\frac{4\left(x-3\right)\left(2x-5\right)}{24}=-\frac{6\left(x-3\right)\left(x-3\right)}{24}\)

\(\Leftrightarrow24\left(x-3\right)-4\left(x-3\right)\left(2x-5\right)+6\left(x-3\right)^2=0\)

\(\Leftrightarrow\left(x-3\right)\left[24-4\left(2x-5\right)+6\left(x-3\right)\right]=0\)

\(\Leftrightarrow\left(x-3\right)\left(24-8x+20+6x-18\right)=0\)

\(\Leftrightarrow\left(x-3\right)\left(26-2x\right)=0\)

\(\Leftrightarrow2\left(x-3\right)\left(13-x\right)=0\)

\(\Leftrightarrow\left[\begin{matrix}x-3=0\\13-x=0\end{matrix}\right.\)

\(\Leftrightarrow\left[\begin{matrix}x=3\\x=13\end{matrix}\right.\)

Vậy tập nghiệm của pt là \(S=\left\{3;13\right\}\)

a) \(x^4+2x^3-12x^2-13x+42=0\)

\(\Leftrightarrow x^4+3x^3-x^3-3x^2-9x^2-27x+14x+42=0\)

\(\Leftrightarrow x^3\left(x+3\right)-x^2\left(x+3\right)-9x\left(x+3\right)+14\left(x+3\right)=0\)

\(\Leftrightarrow\left(x+3\right)\left(x^3-x^2-9x+14\right)=0\)

\(x^4+2x^3+5x^2+4x-12=0\)

\(\Leftrightarrow x^4-x^3+3x^3-3x^2+8x^2-8x^2+12x-12=0\)

\(\Leftrightarrow x^3\left(x-1\right)+3x^2\left(x-1\right)+8x\left(x-1\right)+12\left(x-1\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(x^3+3x^2+8x+12\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(x^3+2x^2+x^2+2x+6x+12\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left[x^2\left(x+2\right)+x\left(x+2\right)+6\left(x+2\right)\right]=0\)

\(\Leftrightarrow\left(x-1\right)\left(x+2\right)\left(x^2+x+6\right)=0\)

Ta có:

\(x^2+x+6=x^2+2.x.\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{23}{4}=\left(x+\dfrac{1}{2}\right)^2+\dfrac{23}{4}>0\)

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

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

Vậy...........

b)\(\left(x-1\right)\left(x+2\right)\left(x+4\right)\left(x+7\right)=16\)

\(\Leftrightarrow\left(x-1\right)\left(x+7\right)\left(x+2\right)\left(x+4\right)=16\)

\(\Leftrightarrow\left(x^2+6x-7\right)\left(x^2+6x+8\right)-16=0\)

Đặt \(x^2+6x+0,5=t\)

\(\Rightarrow\left(t-7,5\right)\left(t+7,5\right)-16=0\)

\(\Rightarrow t^2-56,25-16=0\)

\(\Leftrightarrow t^2-72,25=0\)

\(\Leftrightarrow\left(t-\dfrac{17}{2}\right)\left(t+\dfrac{17}{2}\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}t=\dfrac{17}{2}\\t=-\dfrac{17}{2}\end{matrix}\right.\)

Xét \(t=\dfrac{17}{2}\Rightarrow x^2+6x+0,5=\dfrac{17}{2}\)

\(\Leftrightarrow x^2+6x-8=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-3+\sqrt{17}\\x=-3-\sqrt{17}\end{matrix}\right.\)

TT xét \(t=-\dfrac{17}{2}\Rightarrow x=\)-3

bai 1

1 thay k=0 vao pt ta co 4x^2-25+0^2+4*0*x=0

<=>(2x)^2-5^2=0

<=>(2x+5)*(2x-5)=0

<=>2x+5=0 hoăc 2x-5 =0 tiếp tục giải ý 2 tương tự

Bài 1: 

c) |2x - 1| = x + 2

<=> 2x - 1 = +(x + 2) hoặc -(x + 2)

* 2x - 1 = x + 2      

<=> 2x - x = 2 + 1

<=> x = 3

* 2x - 1 = -(x + 2)

<=> 2x - 1 = x - 2

<=> 2x - x = -2 + 1

<=> x = -1

Vậy.....

cái bài này tìm nghiệm là ra mà bạn

câu trả lời của thu hương rất hay!

Mình làm được khổ nỗi lại chưa biết nghiệm là gì? @ thu hương có thể giải thích cho minh không

 hiihhi  

a, \(5\left|2x-1\right|-3=7\Leftrightarrow5\left|2x-1\right|=10\Leftrightarrow\left|2x-1\right|=2\)

TH1 : \(2x-1=2\Leftrightarrow x=\frac{3}{2}\)

TH2 : \(2x-1=-2\Leftrightarrow x=-\frac{1}{2}\)

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

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

c, \(\frac{2x-3}{2}< \frac{1-3x}{-5}\Leftrightarrow\frac{2x-3}{2}+\frac{1-3x}{5}< 0\)

\(\Leftrightarrow\frac{10x-15+2-6x}{10}< 0\Rightarrow4x-13< 0\Leftrightarrow x< \frac{13}{4}\)

B1.a/ (x-2)(x^2+2x+2)

     b/ (x+1)(x+5)(x+2)

     c/ (x+1)(x^2+2x+4)

B2.

1a) x³ - 2x - 4 = 0

<=> (x³ - 4x) + (2x - 4) = 0

<=> x(x² - 4) + 2(x - 2) = 0

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

<=> (x - 2)(x² + 2x + 2) = 0

<=> x - 2 = 0 (vì x² + 2x + 2 \(\ne\)0)

<=> x = 2

Vậy S = {2}

b) x³ + 8x² + 17x + 10 = 0

<=> (x³ + 5x²) + (3x² + 15x) + (2x + 10) = 0

<=> x²(x + 5) + 3x(x + 5) + 2(x + 5) = 0

<=> (x² + 3x + 2)(x + 5) = 0

<=> (x² + x + 2x + 2)(x + 5) = 0

<=> (x + 1)(x + 2)(x + 5) = 0

<=> x + 1 = 0 hoặc x + 2 = 0 hoặc x + 5 = 0

<=> x = -1 hoặc x = -2 hoặc x = -5

Vậy S = {-1; -2; -5}

c) x³ + 3x² + 6x + 4 = 0

<=> (x³ + x²) + (2x² + 2x) + (4x + 4) = 0

<=> x²(x + 1) + 2x(x + 1) + 4(x + 2) = 0

<=> (x² + 2x + 4)(x + 2) = 0

<=> x + 2 = 0

<=> x = -2

Vậy S = {-2}