\(TH_1:x\ge0\Leftrightarrow x^3\ge0\Leftrightarrow VT>0\left(loại\right)\)

\(TH_2:x< 0\)

Với \(x=-1\Leftrightarrow VT=4\cdot9\cdot14\cdot29>0\left(loại\right)\)

Với \(x=-2\Leftrightarrow VT=-3\cdot2\cdot7\cdot23< 0\left(nhận\right)\)

Với \(x=-3\Leftrightarrow VT=-22\left(-17\right)\left(-12\right)\cdot3< 0\left(nhận\right)\)

Với \(x< -4\Leftrightarrow x^3< -64\Leftrightarrow x^3+5< x^3+10< x^3+15< x^3+30< 0\)

Do đó cả 4 thừa số trong tích đều âm nên tích này luôn dương

Vậy \(x\in\left\{-2;-3\right\}\)

giải

ta có :

\(x1+x2+x3+x4+x5=0\)

\(\left(x1+x2\right)+\left(x3+x4\right)+x5=0\)

\(\Rightarrow2+2+x5=0\Rightarrow x5=-4\)

mà \(x4+x5=2\Rightarrow x4+-4=2\Rightarrow x4=6\)

mặt khác : \(x3+x4=2\Rightarrow x3+6=2\Rightarrow x3=-4\)

vậy : x5 = -4 , x4 = 6 , x3 = -4

Ta có : \(\left\{{}\begin{matrix}x_1+x_2=2\left(I\right)\\x_3+x_4=2\left(II\right)\\x_4+x_5=2\left(III\right)\\x_1+x_2+x_3+x_4+x_5=5\left(IV\right)\end{matrix}\right.\)

Thay (I) và (II) vào (IV) ta được : 2+2+x5=5 => x5=1

Thay x5=1 vào (III) ta được: x4=1

Thay x4=1 vào (II) ta được: x3=1

Vậy x3=x4=x5=1

a) x = 4                

b) x = 3     

c) x = 2                

d) x = 1. 

\(259-51\left|4x+3\right|=\left(-10\right).3+10\)

\(\Leftrightarrow259-51\left|4x+3\right|=-30+10\)

\(\Leftrightarrow259-51\left|4x+3\right|=-20\)

\(\Leftrightarrow-51\left|4x+3\right|=-20-259\)

\(\Leftrightarrow-51\left|4x+3\right|=-279\)

\(\Leftrightarrow\left|4x+3\right|=\frac{279}{51}\)

\(\Leftrightarrow\orbr{\begin{cases}4x+3=\frac{93}{17}\\4x+3=-\frac{93}{17}\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=\frac{21}{34}\\x=-\frac{36}{17}\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=\frac{21}{34}\\x=-\frac{36}{17}\end{cases}}\)

1: \(=x^2+1\)

3: \(=\left(x-y-z\right)^2\)

a. (3x - 1)² - (x + 3)² = 0

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

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

\(\Leftrightarrow4x+2=0\)  hoặc  \(2x-4=0\)

1. \(4x+2=0\Leftrightarrow4x=-2\Leftrightarrow x=-\dfrac{1}{2}\)

2. \(2x-4=0\Leftrightarrow2x=4\Leftrightarrow x=2\)

S=\(\left\{-\dfrac{1}{2};2\right\}\)

b. \(x^3=\dfrac{x}{49}\)

\(\Leftrightarrow49x^3=x\)

\(\Leftrightarrow49x^3-x=0\)

\(\Leftrightarrow x\left(49x^2-1\right)=0\)

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

\(\Leftrightarrow x=0\) hoặc  \(7x+1=0\) hoặc \(7x-1=0\)

1. x=0

2. \(7x+1=0\Leftrightarrow7x=-1\Leftrightarrow x=-\dfrac{1}{7}\)

3. \(7x-1=0\Leftrightarrow7x=1\Leftrightarrow x=\dfrac{1}{7}\)

*Cách khác:

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

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

\(\Leftrightarrow\left[{}\begin{matrix}3x-1=-x-3\\3x-1=x+3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}4x=-2\\2x=4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{1}{2}\\x=2\end{matrix}\right.\)

Vậy: \(S=\left\{-\dfrac{1}{2};2\right\}\)