a) x(x-3)+(x-3)=0

<=>(x-3)(x+1)=0

<=>x-3=0 hoặc x+1=0

<=>x=3 hoặc x=-1

b) 7x(x-5)-x+5=0

<=>(7x-1)(x-5)=0

<=>7x-1=0 hoặc x-5=0

<=>x=1/7 hoặc x=5

a: Ta có: \(x\left(x-3\right)+\left(x-3\right)=0\)

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

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

b: Ta có: \(7x\left(x-5\right)-x+5=0\)

\(\Leftrightarrow\left(x-5\right)\left(7x-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=\dfrac{1}{7}\end{matrix}\right.\)

a) \(\left(x^2-3x\right)\left(x^2+7x+10\right)=216\Rightarrow x\left(x-3\right)\left(x+2\right)\left(x+5\right)=216\)

\(\Rightarrow x\left(x+2\right)\left(x-3\right)\left(x+5\right)=216\Rightarrow\left(x^2+2x\right)\left(x^2+2x-15\right)=216\)

Đặt \(t=x^2+2x\Rightarrow\) pt trở thành \(t\left(t-15\right)=216\Rightarrow t^2-15t-216=0\)

\(\Rightarrow\left(t+9\right)\left(t-24\right)=0\Rightarrow\left[{}\begin{matrix}t=-9\\t=24\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x^2+2x=-9\\x^2+2x=24\end{matrix}\right.\)

\(TH_1:x^2+2x=-9\Rightarrow x^2+2x+9=0\Rightarrow\left(x+1\right)^2+8=0\) (vô lý)

\(TH_2:x^2+2x=24\Rightarrow x^2+2x-24=0\Rightarrow\left(x-4\right)\left(x+6\right)=0\)

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

b) \(\left(2x^2-7x+3\right)\left(2x^2+x-3\right)+9=0\)

\(\Rightarrow\left(x-3\right)\left(2x-1\right)\left(x-1\right)\left(2x+3\right)+9=0\)

\(\Rightarrow\left(x-3\right)\left(2x+3\right)\left(x-1\right)\left(2x-1\right)+9=0\)

\(\Rightarrow\left(2x^2-3x-9\right)\left(2x^2-3x+1\right)+9=0\)

Đặt \(t=2x^2-3x-9\Rightarrow\) pt trở thành \(t\left(t+10\right)+9=0\)

\(\Rightarrow t^2+10t+9=0\Rightarrow\left(t+1\right)\left(t+9\right)=0\Rightarrow\left[{}\begin{matrix}t=-1\\t=-9\end{matrix}\right.\)

\(TH_1:t=-1\Rightarrow2x^2-3x-9=-1\Rightarrow2x^2-3x-8=0\)

\(\Delta=\left(-3\right)^2-4\left(-8\right).2=73\Rightarrow\left[{}\begin{matrix}x=\dfrac{-b-\sqrt{\Delta}}{2a}=\dfrac{3-\sqrt{73}}{4}\\x=\dfrac{-b+\sqrt{\Delta}}{2a}=\dfrac{3+\sqrt{73}}{4}\end{matrix}\right.\)

\(TH_2:t=-9\Rightarrow2x^2-3x-9=-9\Rightarrow2x^2-3x=0\Rightarrow x\left(2x-3\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{3}{2}\end{matrix}\right.\)

Đề yêu cầu gì em?

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

\(x^2-7x+12=\left(x-2\right)\left(x-5\right)\)

\(x^2+x-12=\left(x-5\right)\left(x+6\right)\)

\(x^2-9x+20=\left(x-4\right)\left(x-5\right)\)

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

\(4x^2-7x-2=4\left(x-2\right)\left(x+\dfrac{1}{4}\right)\)

\(4x^2+15x+9=4\left(x+\dfrac{3}{4}\right)\left(x+3\right)\)

a) x=0

b) x=0

c) x=0

d)x=x

a b c d 

x=x

\(x^2-6x+5=0\)

\(\Leftrightarrow x^2-x-5x+5=0\)

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

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

\(\Leftrightarrow\orbr{\begin{cases}x-1=0\\x-5=0\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=1\\x=5\end{cases}}\)

\(2x^2+7x+9=0\)

Đề sai??

\(4x^2-7x+3=0\)

\(\Leftrightarrow4x^2-4x-3x+3=0\)

\(\Leftrightarrow4x\left(x-1\right)-3\left(x-1\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(4x-3\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x-1=0\\4x-3=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=1\\x=\frac{3}{4}\end{cases}}\)

\(2\left(x+5\right)=x^2+5x\)

\(\Leftrightarrow2x+10=x^2+5x\)

\(\Leftrightarrow x^2+5x-2x-10=0\)

\(\Leftrightarrow x^2+3x-10=0\)

\(\Leftrightarrow x^2+5x-2x-10=0\)

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

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

\(\Leftrightarrow\orbr{\begin{cases}x+5=0\\x-2=0\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=-5\\x=2\end{cases}}\)

X bằng 5 hoặc -2

x = -2

(x-5)(6x + 12)=0
=> x - 5 = 0 hoặc 6x + 12 = 0 nên ta có 2 trường hợp
TH1 :
x - 5 = 0
x      = 0 + 5
x      = 5
TH2 :
6x + 12 = 0 
6x         = 0 - 12 
6x         = -12
  x         = -12 : 6
  x         = -2
Vậy x có thể bằng 5 hoặc -2
 

Bài 2:

a: =>2x^2-4x+1=x^2+x+5

=>x^2-5x-4=0

=>\(x=\dfrac{5\pm\sqrt{41}}{2}\)

b: =>11x^2-14x-12=3x^2+4x-7

=>8x^2-18x-5=0

=>x=5/2 hoặc x=-1/4

bài lạ thật

ý bạn là như thế này đúng không ạ:

a/ \(x^2-6x+5=0\)

\(x^2-5x-x+5=0\)

\(x\left(x-5\right)-\left(x-5\right)=0\)

\(\left(x-5\right)\left(x-1\right)=0\)

\(\orbr{\begin{cases}x-5=0\rightarrow x=5\\x-1=0\rightarrow x=1\end{cases}}\)

b/\(2x^2+7x+9=0\)

?!

c/ \(4x^2-7x+3=0\)

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

\(4x\left(x-1\right)-3\left(x-1\right)=0\)

\(\left(x-1\right)\left(4x-3\right)=0\)

\(\orbr{\begin{cases}x-1=0\Rightarrow x=1\\4x-3=0\Rightarrow x=\frac{3}{4}\end{cases}}\)

d/ \(2\left(x+5\right)=2x+10\)

-,- mik ko rõ đề ạ, sai thì ibox ạ.Cảm ơn

x2−6x+5=0

2x2+7x+9=0

4x2−7x+3=0

2(x+5)=x2+5x