a) $(x-3)^2-(x+2)(x-2)=-5$

$\Rightarrow x^2-2\cdot x\cdot3+3^2-(x^2-2^2)=-5$

$\Rightarrow x^2-6x+9-(x^2-4)=-5$

$\Rightarrow x^2-6x+9-x^2+4=-5$

$\Rightarrow-6x+13=-5$

$\Rightarrow-6x=-18$

$\Rightarrow x=3$

b) $x^3-2x^2-4x+8=0$

$\Rightarrow(x^3-2x^2)-(4x-8)=0$

$\Rightarrow x^2(x-2)-4(x-2)=0$

$\Rightarrow (x^2-4)(x-2)=0$

$\Rightarrow (x^2-2^2)(x-2)=0$

$\Rightarrow (x-2)(x+2)(x-2)=0$

$\Rightarrow (x-2)^2(x+2)=0$

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

$\text{#}Toru$

3) \(x\left(x-4\right)+\left(x-4\right)^2=0\Leftrightarrow\left(x-4\right)\left(x+x-4\right)=0\Leftrightarrow2\left(x-4\right)\left(x-2\right)=0\)

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

4x.(x+1)-8(x+1)=0

(4x-8)(x+1)=0

suy ra x=2 hoặc x=-1

1) \(4x\left(x+1\right)=8\left(x+1\right)\Leftrightarrow4x^2+4x=8x+8\Leftrightarrow4x^2-4x-8=0\Leftrightarrow x^2-x-2=0\Leftrightarrow\left(x-2\right)\left(x+1\right)=0\)

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

a) \(\left(x-3\right)^2-4=0\)

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

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

\(\left(x-3\right)^2=\pm4\)

\(\left(x-3\right)^2=\pm2^2\)

\(\orbr{\begin{cases}x-3=2\\x-3=-2\end{cases}}\)

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

b) \(\left(2x+3\right)^2-\left(2x+1\right)\left(2x-1\right)=22\)

\(4x^2+12x+9-4x^2+1=22\)

\(12x+10=22\)

\(12x=22-10\)

\(12x=12\)

\(x=1\)

c) \(\left(4x+3\right)\left(4x-3\right)-\left(4x-5\right)^2=16\)

\(16x^2-9-16x^2+40x-25=16\)

\(-34+40x=16\)

\(40x=16+34\)

\(40x=50\)

\(x=\frac{50}{40}=\frac{5}{4}\)

d) \(x^3-9x^2+27x-27=-8\)

\(x^3-9x^2+27x-27+8=0\)

\(x^3-9x^2+27x-19=0\)

\(\left(x^2-8x+19\right)\left(x-1\right)=0\)

Vì \(\left(x^2-8x+19\right)>0\) nên:

\(x-1=0\)

\(x=1\)

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

\(x^3+2x^2+x+x^2+2x+1-x^2-3x^2=2\)

\(3x+1=2\)

\(3x=2-1\)

\(3x=1\)

\(x=\frac{1}{3}\)

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

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

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

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

Vậy \(x=1;-3\)

b) \(x^2-4x+8=2x-1\)

\(\Leftrightarrow x^2-4x+8-2x+1=0\)

\(\Leftrightarrow x^2-6x+9=0\)

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

\(\Leftrightarrow x-3=0\)

\(\Leftrightarrow x=3\)

Vậy x=3

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

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

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

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

Vậy \(x=1;-3\)

b)    \(x^2-4x+8=2x-1\)

\(\Leftrightarrow x^2-4x+8-2x+1=0\)

\(\Leftrightarrow x^2-6x+9=0\)

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

\(\Leftrightarrow x-3=0\)

\(\Leftrightarrow x=3\)

Vậy \(x=3\)

yggucbsgfuyvfbsudy

????????

(2x-3)²-(x+5)²=0

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

<=>(x-8)(3x+2)=0

<=>x-8=0 hoặc 3x+2=0

<=>x=8 hoặc x=-2/3

(2x-3)2
-(x+5)2=0
<=>(2x-3-x-5)(2x-3+x+5)=0
<=>(x-8)(3x+2)=0
<=>x-8=0 hoặc 3x+2=0
<=>x=8 hoặc x=-2/3

chcú cậu hok tốt @_@

(2x-3)² - (x+5)² = 0
<=>(2x-3-x-5)(2x-3+x+5)=0
<=>(x-8)(3x+2)=0
<=>x-8=0 hoặc 3x+2=0
<=>x=8 hoặc x=-2/3

\(a,\Leftrightarrow x^2+6x+9-x^2+3x+10=1\\ \Leftrightarrow9x=-18\Leftrightarrow x=-2\\ b,\Leftrightarrow4x^2-4x+1-4x^2+17x+15=3\\ \Leftrightarrow13x=-13\Leftrightarrow x=-1\\ c,\Leftrightarrow3x\left(x-2\right)+4\left(x-2\right)=0\\ \Leftrightarrow\left(3x+4\right)\left(x-2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{4}{3}\\x=2\end{matrix}\right.\\ d,\Leftrightarrow2x\left(3x+5\right)-6\left(3x+5\right)=0\\ \Leftrightarrow\left(x-3\right)\left(3x+5\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=3\\x=-\dfrac{5}{3}\end{matrix}\right.\)

1) \(\Rightarrow10x-16-12x+15=12x-16+11\)

\(\Rightarrow14x=4\Rightarrow x=\dfrac{2}{7}\)

2) \(\Rightarrow4x^2+4x+1-4x^2+13x-3-15=0\)

\(\Rightarrow17x=17\Rightarrow x=1\)

3) \(\Rightarrow\left(3x-1\right)\left(2x-7+6x-5\right)=0\)

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

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

2: Ta có: \(\left(2x+1\right)^2-\left(4x-1\right)\left(x-3\right)-15=0\)

\(\Leftrightarrow4x^2+4x+1-4x^2+12x+x-3-15=0\)

\(\Leftrightarrow17x=17\)

hay x=1