\(x^3+9x=0\)

<=> \(x\left(x^2+9\right)=0\)

<=> \(\orbr{\begin{cases}x=0\\x^2+9=0\end{cases}}\)

<=> \(\orbr{\begin{cases}x=0\\x\in\varnothing\end{cases}}\)

<=> \(x=0\)

\(9x^2-4-2\left(3x-2\right)^2=0\)

<=> \(\left(9x^2-4\right)-2\left(3x-2\right)^2=0\)

<=> \(\left[\left(3x\right)^2-2^2\right]-2\left(3x-2\right)^2=0\)

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

<=> \(\left(3x-2\right)\left[\left(3x+2\right)-2\left(3x-2\right)\right]=0\)

<=> \(\left(3x-2\right)\left(3x+2-6x+4\right)=0\)

<=> \(\left(3x-2\right)\left(-3x+6\right)=0\)

<=> \(\left(3x-2\right)3\left(-x+2\right)=0\)

<=> \(3\left(3x-2\right)\left(2-x\right)=0\)

<=> \(\orbr{\begin{cases}3x-2=0\\2-x=0\end{cases}}\)

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

<=> \(\orbr{\begin{cases}x=\frac{2}{3}\\x=2\end{cases}}\)

\(\left(x^3-x^2\right)-4x+8x-4=0\)

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

<=> \(x^2\left(x-1\right)+4\left(x-1\right)=0\)

<=> \(\left(x-1\right)\left(x^2+4\right)=0\)

<=> \(\orbr{\begin{cases}x-1=0\\x^2+4=0\end{cases}}\)

<=> \(x=1\)

\(\left(25x^2-10x\right):\left(-5x\right)-3\left(x-2\right)=4\)

<=> \(5x\left(5x-2\right)\left(-\frac{1}{5x}\right)-3\left(x-2\right)=4\)

<=> \(-\left(5x-2\right)-3\left(x-2\right)=4\)

<=> \(\left(5x-2\right)+3\left(x-2\right)=-4\)

<=> \(5x-2+3x-6=-4\)

<=> \(8x-8=-4\)

<=> \(8\left(x-1\right)=-4\)

<=> \(x-1=-\frac{1}{2}\)

<=> \(x=-\frac{3}{2}\)

e) \(\left(9x^2-49\right)+\left(3x+7\right)\left(7x+3\right)=0\)

\(\Rightarrow\text{[}\left(3x\right)^2-7^2\text{]}+\left(3x+7\right)\left(7x+3\right)=0\)

\(\Rightarrow\left(3x-7\right)\left(3x+7\right)+\left(3x+7\right)\left(7x+3\right)=0\)

\(\Rightarrow\left(3x+7\right)\text{[}\left(3x-7\right)+\left(7x+3\right)\text{]}=0\)

\(\Rightarrow\left(3x+7\right)\left(3x-7+7x+3\right)=0\)

\(\Rightarrow\left(3x+7\right)\left(10x-4\right)=0\)

=> 2 TH

*3x+7=0               *10x-4=0

=>3x=-7               =>10x=4

=>x=-7/3              =>x=4/10=2/5

vậy x=-7/3 hoặc x=2/5

g) \(\left(x-4\right)^2=\left(2x-1\right)^2\)

\(\Rightarrow\left(x-4\right)^2-\left(2x-1\right)^2=0\)

\(\Rightarrow\left(x-4-2x+1\right)\left(x-4+2x-1\right)=0\)

\(\Rightarrow\left(-x-3\right)\left(3x-5\right)=0\)

\(\Rightarrow-\left(x+3\right)\left(3x-5\right)=0\)

=> 2 TH

*-(x+3)=0          *3x-5=0

=>-x=-3            =>3x=5  

=x=3                =>x=5/3

h)\(x^2-x^2+x-1=0\)

\(\Rightarrow0+x-1=0\)

\(\Rightarrow x-1=0\)

=>x=0+1

=>x=1

vậy x=1

k, x(x+ 16) - 7x - 42 = 0

=>x^2+16x-7x-42=0

=>x^2+9x-42=0

vì x^2>0

do đó x^2+9x-42>0

nên o có gt nào của x t/m y/cầu đề bài

m)x^2+7x+12=0

=>x^2+3x++4x+12=0

=>x(x+3)+4(x+3)=0

=>(x+4).(x+3)=0

=>2 TH

=> *x+4=0

=>x=-4

vậy x=-4

*x+3=0

=>x=-3

vậy x=-3

n)x^2-7x+12=0

=>x^2-4x-3x+12=0

=>x(x-4)-3(x-4)=0

=>(x-3).(x-4)=0

=>2 TH

*x-3=0=>x=0+3=>x=3

*x-4=0=>x=0+4=>x=4

vậy x=3 hoặc x=4

a)(3x−3)(5−21x)+(7x+4)(9x−5)=44⇔15x−63x2−15+63x+63x2−35x+36x−20=44⇔79x−35=44⇔79x=79⇒x=1a)(3x−3)(5−21x)+(7x+4)(9x−5)=44⇔15x−63x2−15+63x+63x2−35x+36x−20=44⇔79x−35=44⇔79x=79⇒x=1

b)(x+1)(x+2)(x+5)−x2(x+8)=27⇔x2+2x+x+2(x+5)−x3−8x2=27⇔x2(x+5)+2x(x+5)+x(x+5)+2(x+5)−x3−8x2=27⇔x3+5x2+2x2+10x+x2+5x+2x+10−x3−8x2=27⇔17x+10=27⇔17x=17⇒x=1

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

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

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

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

\(\Leftrightarrow\orbr{\begin{cases}x^2=0\\\left(x-2\right)^2=0\end{cases}}\)\(\Leftrightarrow\orbr{\begin{cases}x=0\\x-2=0\end{cases}}\)\(\Leftrightarrow\orbr{\begin{cases}x=0\\x=2\end{cases}}\)

\(b,\)\(x^2+5x+4=0\)

\(\Leftrightarrow x^2+x+4x+4=0\)

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

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

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

\(c,\)\(9x-6x^2-3=0\)

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

\(\Leftrightarrow2x^2-3x+1=0\)

\(\Leftrightarrow2x^2-2x-x+1=0\)

\(\Leftrightarrow2x.\left(x-1\right)-\left(x-1\right)\)

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

\(\Leftrightarrow\orbr{\begin{cases}x-1=0\\2x-1=0\end{cases}}\)\(\Leftrightarrow\orbr{\begin{cases}x=1\\2x=1\end{cases}}\)\(\Leftrightarrow\orbr{\begin{cases}x=1\\x=\frac{1}{2}\end{cases}}\)

\(d,\)\(2x^2+5x+2=0\)

\(\Leftrightarrow2x^2+4x+x+2=0\)

\(\Leftrightarrow2x.\left(x+2\right)+\left(x+2\right)=0\)

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

\(\Leftrightarrow\orbr{\begin{cases}x+2=0\\2x+1=0\end{cases}}\)\(\Leftrightarrow\orbr{\begin{cases}x=-2\\2x=-1\end{cases}}\)\(\Leftrightarrow\orbr{\begin{cases}x=-2\\x=-\frac{1}{2}\end{cases}}\)

a) x³ + 3x² + 3x + 1 = 64

=> (x + 1)³ = 64

=> (x + 1)³ = 4³

=> x + 1 = 4 => x = 3

b) x³ + 6x² + 9x = 4x

=> x³ + 6x² + 9x - 4x = 0

=> x³ + 6x² + 5x = 0

=> x³ + 5x² + x² + 5x = 0

=> x²(x + 5) + x(x + 5) = 0

=> (x + 5)(x² + x) = 0

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

=> \(\hept{\begin{cases}x=-5\\x=0\\x=-1\end{cases}}\)

c) 4(x - 2)² = (x + 2)²

=> 4(x² - 4x + 4) = x² + 4x + 4

=> 4x² - 16x + 16 = x² + 4x + 4

=> 4x² - 16x + 16 - x² - 4x - 4 = 0

=> 3x² - 20x + 12 = 0

=> 3x² - 18x - 2x + 12 = 0

=> 3x(x - 6) - 2(x - 6) = 0

=> (x - 6)(3x - 2) = 0

=> \(\orbr{\begin{cases}x=6\\x=\frac{2}{3}\end{cases}}\)

d) x⁴ - 16x² = 0

=> x²(x² - 16) = 0

=> \(\orbr{\begin{cases}x^2=0\\x^2=16\end{cases}}\Rightarrow\orbr{\begin{cases}x=0\\x=\pm4\end{cases}}\)

e) x⁴ - 4x³ + x² - 4x = 0

=> x⁴ + x² - 4x³ - 4x = 0

=> x²(x² + 1) - 4x(x² + 1) = 0

=> (x² - 4x)(x² + 1) = 0

=> x(x - 4)(x² + 1) = 0

=> \(\orbr{\begin{cases}x=0\\x=4\end{cases}}\)(vì x² + 1 \(\ge\)1 > 0 \(\forall\)x)

f) x³ + x = 0 => x(x²  + 1) = 0 => x = 0 (vì x² + 1 \(\ge1>0\forall\)x)

\(a,x^3+3x^2+3x+1=64\)

\(\left(x+1\right)^3=64\)

\(\left(x+1\right)^3=4^3\)

\(x+1=4\)

\(x=3\)

\(\left(3x-5\right)\left(-2x-7\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}3x-5=0\\-2x-7=0\end{cases}\Leftrightarrow\orbr{\begin{cases}3x=5\\-2x=7\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=\frac{5}{3}\\x=\frac{-7}{2}\end{cases}}}\)

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

\(\Leftrightarrow9x^2-1=2x-3+6x^2-9x\)

\(\Leftrightarrow9x^2-1=-7x-3+6x^2\)

\(\Leftrightarrow9x^2-1+7x+3-6x^2=0\)

\(\Leftrightarrow3x^2+2+7x=0\)

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

\(\Leftrightarrow3x\left(x+2\right)+\left(x+2\right)=0\)

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

\(\Leftrightarrow\orbr{\begin{cases}x+2=0\\3x+1=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-2\\x=-\frac{1}{3}\end{cases}}\)

a) Ta có : x³ - x = 0

=> x(x² - 1) = 0

=> \(\orbr{\begin{cases}x=0\\x^2=1\end{cases}}\Rightarrow\orbr{\begin{cases}x=0\\x=\pm1\end{cases}}\)

Vậy \(x\in\left\{0;1;-1\right\}\)

b) x² + 4x = 0

=> x(x + 4) = 0

=> \(\orbr{\begin{cases}x=0\\x=-4\end{cases}}\)

Vậy \(x\in\left\{0;-4\right\}\)

c) 9x² - 1 = 0

=> 9x² = 1

=> x² = \(\frac{1}{9}\)

=> \(\orbr{\begin{cases}x=\frac{1}{3}\\x=-\frac{1}{3}\end{cases}}\)

Vậy \(x\in\left\{\frac{1}{3};-\frac{1}{3}\right\}\)

d) 5x² - 10x + 5 = 0

=> 5x² - 5x - 5x + 5 = 0

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

=> 5(x - 1)² = 0

=> (x - 1)² = 0

=> x - 1 = 0

=> x = 1

e) x² + 6x + 5 = 0

=> x² + 6x + 9 - 4 = 0

=> (x + 3)² = 4

=> \(\orbr{\begin{cases}x+3=2\\x+3=-2\end{cases}}\Rightarrow\orbr{\begin{cases}x=-1\\x=-5\end{cases}}\)

Vậy \(x\in\left\{-1;-5\right\}\)

a, \(x^3-x=0\Leftrightarrow x\left(x^2-1\right)=0\Leftrightarrow\orbr{\begin{cases}x=0\\x=\pm1\end{cases}}\)

b, \(5x^2-10x+5=0\)

\(\Leftrightarrow5x\left(x-1\right)^2=0\Leftrightarrow\orbr{\begin{cases}x=0\\x=1\end{cases}}\)

\(a.x^4-16x^2=0\Leftrightarrow\left(x^2+4x\right)\left(x^2-4x\right)=0\)

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

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

\(b.\left(x-5\right)^3-x+5=0\)

\(\Leftrightarrow\left(x-5\right)^3-\left(x-5\right)=0\)

\(\Leftrightarrow\left(x-5\right)\left[\left(x-5\right)^2-1\right]=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-5=0\\\left(x-5\right)^2-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\\left(x-5\right)^2=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\x=6\end{matrix}\right.\)

a) x⁴ - 16x² = 0

<=> x² ( x² - 16 ) = 0

<=> \(\left[{}\begin{matrix}x^2=0\\x^2-16=0\end{matrix}\right.\) <=> \(\left[{}\begin{matrix}x=0\\x=-4\\x=4\end{matrix}\right.\)

Vậy...

b) ( x - 5)³ - x + 5 = 0

<=> ( x - 5)³ - (x - 5) = 0

<=> (x - 5) [ (x - 5)² - 1] =0

<=> \(\left[{}\begin{matrix}x-5=0\\\left(x-5\right)^2-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\\left(x-5\right)^2=1\end{matrix}\right.\)

<=> \(\left[{}\begin{matrix}x=5\\x-5=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\x=6\end{matrix}\right.\)

Vậy...

c) 5(x - 2) = x² - 4

<=> 5(x - 2) - (x² - 4) = 0

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

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

<=> \(\left[{}\begin{matrix}x=2\\x=3\end{matrix}\right.\)

Vậy...

d) x - 3 = (3 - x)²

<=> x - 3 - (x - 3)² = 0

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

<=> (x - 3)( 4 - x ) = 0

<=> \(\left[{}\begin{matrix}x=3\\x=4\end{matrix}\right.\)

Vậy...

e) x² (x - 5) + 5 - x = 0

<=> x² (x - 5) - (x - 5) = 0

<=> (x² - 1)( x - 5) = 0

<=> \(\left[{}\begin{matrix}\left(x-1\right)\left(x+1\right)=0\\x-5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-1\\x=5\end{matrix}\right.\)

,

1)3.x^2 - 75 = 0

3.x^2 - 3.25 = 0

3.(x^2-25)=0

x^2-5^2=0

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

=> x-5=0 hoặc x+5=0

=> x=5 hoặc x=-5

1) \(3x^2-75=0\)

\(\Leftrightarrow3\left(x^2-25\right)=0\)

\(\Leftrightarrow x^2-25=0\)

\(\Leftrightarrow x^2=25\)

\(\Leftrightarrow x=\pm\sqrt{25}=\pm5\)

2) \(x^3+9x^2+27x+27=0\)

\(\Leftrightarrow\left(x+3\right)^3=0\)

\(\Leftrightarrow x+3=0\Leftrightarrow x=-3\)

3) \(x^3+3x^2+3x=0\)

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

\(\Leftrightarrow\left(x+1\right)^3=1^3\)

\(\Leftrightarrow x+1=1\Leftrightarrow x=0\)

b) \(7x\left(x-2\right)-\left(x-2\right)=0\) 

<=>  \(\left(7x-1\right)\left(x-2\right)=0\)

=> x=1/7  hoặc x=2

c) <=>  (2x-1)³   =0 

=> x=1/2

d)<=>  \(\left(2x-3\right)\left(2x+3\right)-x\left(2x-3\right)=0\)

<=>  \(\left(2x-3\right)\left(x+3\right)=0\)

=> x=3/2  hoặc x=-3

e) <=>\(x^2\left(x+5\right)+9\left(x+5\right)=0\)

<=> \(\left(x+5\right)\left(x^2+9\right)=0\)

=> x=-5

f) \(x^3-6x^2-x+30=0\)

<=>\(x^3+2x^2-8x^2-16x+15x+30=0\)

<=>\(x^2\left(x+2\right)-8x\left(x+2\right)+15\left(x+2\right)=0\)

<=>\(\left(x+2\right)\left(x^2-5x-3x+15\right)=0\)

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

=> x=-2 hoặc x=5 hoặc x=3