a: \(x\in\left\{0;25\right\}\)

c: \(x\in\left\{0;5\right\}\)

a: Ta có: \(\left(x^2+2\right)\left(x-4\right)-\left(x+2\right)^3=-16\)

\(\Leftrightarrow x^3-4x^2+2x-8-x^3-6x^2-12x-8=-16\)

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

\(\Leftrightarrow-10x\left(x+1\right)=0\)

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

c: Ta có: \(x^3+3x^2+3x+28=0\)

\(\Leftrightarrow\left(x+1\right)^3=-27\)

\(\Leftrightarrow x+1=-3\)

hay x=-4

a) Ta có: \(7x^2-28=0\)

\(\Leftrightarrow7\left(x^2-4\right)=0\)

\(\Leftrightarrow7\left(x-2\right)\left(x+2\right)=0\)

mà 7>0

nên (x-2)(x+2)=0

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

Vậy: \(x\in\left\{2;-2\right\}\)

b) Ta có: \(\dfrac{2}{3}x\left(x^2-4\right)=0\)

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

mà \(\dfrac{2}{3}>0\)

nên x(x-2)(x+2)=0

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

Vậy: \(x\in\left\{0;-2;2\right\}\)

c) Ta có: \(2x\left(3x-5\right)-\left(5-3x\right)=0\)

\(\Leftrightarrow2x\left(3x-5\right)+\left(3x-5\right)=0\)

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

\(\Leftrightarrow\left[{}\begin{matrix}3x-5=0\\2x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}3x=5\\2x=-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{3}\\x=-\dfrac{1}{2}\end{matrix}\right.\)

Vậy: \(x\in\left\{\dfrac{5}{3};-\dfrac{1}{2}\right\}\)

d) Ta có: \(\left(2x-1\right)^2-25=0\)

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

\(\Leftrightarrow\left(2x-6\right)\left(2x+4\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}2x-6=0\\2x+4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=6\\2x=-4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-2\end{matrix}\right.\)

Vậy: \(x\in\left\{3;-2\right\}\)

a,7x² - 28 = 0

=> 7x² = 28 => x² = 4 => x = 2

b,2/3x(x² - 4) = 0

=>2/3x(x - 2)(x + 2) = 0

=> x ∈ {0 ; 2 ; -2}

c,2x(3x - 5) - (5 - 3x) = 0

= 2x(3x - 5) + (3x - 5)

= (3x - 5)(2x + 1) = 0

=> x ∈ { 5/3 ; -1/2}

d, (2x - 1)² - 25 = 0

=> (2x - 4)(2x - 6) = 0

=> x ∈ {2 ;3}

a,7x² - 28 = 0

=> 7x² = 28 => x² = 4 => x = 2

b,2/3x(x² - 4) = 0

=>2/3x(x - 2)(x + 2) = 0

=> x ∈ {0 ; 2 ; -2}

c,2x(3x - 5) - (5 - 3x) = 0

= 2x(3x - 5) + (3x - 5)

= (3x - 5)(2x + 1) = 0

=> x ∈ { 5/3 ; -1/2}

d, (2x - 1)² - 25 = 0

=> (2x - 4)(2x - 6) = 0

=> x ∈ {2 ;3}

a) (x + 3)³ - x(3x + 1)²  + (2x + 1)(4x² - 2x + 1) = 28

=> x³ + 9x² + 27x + 27 - x(9x² + 6x + 1) +(2x + 1)[(2x)² - 2.x.1 + 1² ] = 28

=> x³ + 9x² + 27x + 27 - 9x³ - 6x² - x + (2x)³ + 1³ = 28

=> x³ + 9x² + 27x + 27 - 9x³ - 6x² - x + 8x³ + 1 = 28

=> (x³ - 9x³  + 8x³) + (9x² - 6x²) + (27x - x) + (27 + 1) = 28

=> 3x² + 26x + 28 = 28

=> 3x² + 26x = 0

=> 3x² + 26x = 0

=> \(3x\left(x+\frac{26}{3}\right)=0\)

=> 3x = 0 hoặc x + 26/3 = 0

=> x = 0 hoặc x = -26/3

b) \(\left(x^2-1\right)^3-\left(x^4+x^2+1\right)\left(x^2-1\right)=0\)

=> \(x^6-3x^4+3x^2-1-\left(x^6-1\right)=0\)

=> \(x^6-3x^4+3x^2-1-x^6+1=0\)

=> \(\left(x^6-x^6\right)-3x^4+3x^2+\left(-1+1\right)=0\)

=> \(-3x^4+3x^2=0\)

=> \(-\left(3x^4-3x^2\right)=0\)

=> \(3x\left(x^3-x\right)=0\)

=> \(\orbr{\begin{cases}3x=0\\x^3-x=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=0\\x\left(x^2-1\right)=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=0\\x^2-1=0\end{cases}}\)

=> \(\orbr{\begin{cases}x=0\\x=\pm1\end{cases}}\)

a: \(x^3-4x^2-x+4=0\)

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

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

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

=>\(\left[{}\begin{matrix}x-4=0\\x^2-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\x^2=1\end{matrix}\right.\Leftrightarrow x\in\left\{2;1;-1\right\}\)

b: Sửa đề: \(x^3+3x^2+3x+1=0\)

=>\(x^3+3\cdot x^2\cdot1+3\cdot x\cdot1^2+1^3=0\)

=>\(\left(x+1\right)^3=0\)

=>x+1=0

=>x=-1

c: \(x^3+3x^2-4x-12=0\)

=>\(\left(x^3+3x^2\right)-\left(4x+12\right)=0\)

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

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

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

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

d: \(\left(x-2\right)^2-4x+8=0\)

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

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

=>\(\left(x-2\right)\left(x-2-4\right)=0\)

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

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

(Ko chép lại đề)

\(a.\Rightarrow\orbr{\begin{cases}3x+5=0\\4-3x=0\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=-\frac{5}{3}\\x=\frac{4}{3}\end{cases}}\)

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

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

\(\Rightarrow\orbr{\begin{cases}x=\frac{2}{3}\\x=7\end{cases}}\)

\(c.7x^2=28\)

\(x^2=4\)

\(x^2=2^2\)

\(x=\pm2\)

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

\(\Rightarrow\orbr{\begin{cases}2x+1=0\\1+x=0\end{cases}}\)

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

a)\(\left(3x+5\right)\left(4-3x\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}3x+5=0\\4-3x=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=-\frac{5}{3}\\x=\frac{4}{3}\end{cases}}}\)

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

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

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

c) \(7x^2-28=0\)

\(\Leftrightarrow7x^2=28\)

\(\Leftrightarrow7x^2=7.4\)

\(\Leftrightarrow x^2=4\)

\(\Leftrightarrow x=\pm2\)

d)\(\left(2x+1\right)+x\left(2x+1\right)=0\)

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

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

#H

\(\Leftrightarrow x^3+3x^2+3x+1+27=0\\ \Leftrightarrow\left(x+1\right)^3+27=0\\ \Leftrightarrow\left(x+4\right)\left(x^2+2x+1-3x-3+9\right)=0\\ \Leftrightarrow\left(x+4\right)\left(x^2-x+7\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=-4\\\left(x-\dfrac{1}{2}\right)^2+\dfrac{27}{4}=0\left(vn\right)\end{matrix}\right.\Leftrightarrow x=-4\)

a) \(\left(3x+4\right)\left(4-x\right)=0\Rightarrow\orbr{\begin{cases}3x+4=0\\4-x=0\end{cases}}\)

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

\(\Rightarrow x=\left\{\frac{-4}{3};4\right\}\)

b) \(\Rightarrow\orbr{\begin{cases}3\left(x-4\right)=0\\2\left(x-4\right)=0\end{cases}}\)

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

c) => 7x²=0+28

=> x²=28:7

=> x²=4

=> x²=2²= (-2)²

=> x={-2;2}

Bài 2: 

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

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