\(\left(x+1\right)\left(x+2\right)^2\left(x+3\right)\)

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

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

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

\(=\left(x^3+5x^2+8x+4\right)\left(x+3\right)\)

\(=x^4+3x^3+5x^3+15x^2+8x^2+24x+4x+12\)

\(=x^4+8x^3+23x^2+28x+12\)

=(x-y)²-2x+2y+1+2y²-2y+0,5+2003.

=(x-y-1)²+2(y-0,5)²+2003 >0 nên phương trình vô nghiệm.

sao gửi đc vậy ạ

= -2 ( x² + 2x + 1 ) + 32

= -2 ( x +1 )² + 32

= - 2 [ (x + 1 )² - 16 ]

= -2 [ (x + 1 ) ² - 4² ]

= -2 ( x + 1 - 4 ) ( x + 1 + 4)

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

\(-2x^2-4x+30\)

\(=-2\left(x^2+2x+1\right)+32\)

\(=-2\left(x+1\right)^2+32\)

\(=-2\left[\left(x+1\right)^2-16\right]\)

\(=-2\left[\left(x+1\right)^2-4^2\right]\)

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

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

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

<=> \(x\left(x-1\right)-3\left(x-1\right)=0\)

<=> \(\left(x-3\right)\left(x-1\right)=0\)

<=> \(\hept{\begin{cases}x-3=0\\x-1=0\end{cases}}\)

<=> \(\hept{\begin{cases}x=3\\x=1\end{cases}}\)

\(3x\left(x-2\right)+10-5x=0\)

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

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

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

<=> \(\hept{\begin{cases}3x-5=0\\x-2=0\end{cases}}\)

<=> \(\hept{\begin{cases}x=\frac{5}{3}\\x=2\end{cases}}\)

học tốt

       \(-2x^2-4x+30\)

\(=-2x^2-10x+6x+30\)

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

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

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

Chúc bạn học tốt.

x² - 4x - 21

= x² - 2.x . 2  + 4 - 25

= ( x - 2 )² - 5²
= ( x - 2 + 5 ) ( x - 2 - 5 )

= ( x +3 ) ( x -7 )

\(x^2-4x-21\)

\(=x^2-2.x.2+4-25\)

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

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

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