\(a,\Leftrightarrow\left(x-4\right)\left(x^2+5\right)>0\\ \Leftrightarrow x-4>0\left(x^2+5\ge5>0\right)\\ \Leftrightarrow x>4\\ b,\Leftrightarrow\left(x-y\right)\left(3x-5\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=y\left(vô.lí.do.x\ne y\right)\\x=\dfrac{5}{3}\left(tm\right)\end{matrix}\right.\\ \Leftrightarrow S=x^2-x=\dfrac{25}{9}-\dfrac{5}{3}=\dfrac{10}{9}\)

A = - 3\(x\).(\(x-5\)) + 3(\(x^2\) - 4\(x\)) - 3\(x\) - 10

A = - 3\(x^2\) + 15\(x\) + 3\(x^2\) - 12\(x\) - 3\(x\) - 10

A = (- 3\(x^2\) + 3\(x^2\)) + (15\(x\) - 12\(x\) - 3\(x\)) - 10

A = 0 + (3\(x-3x\)) - 10

A = 0  - 10

A = - 10 

\(a,\Rightarrow\left(2x-5\right)^2+2\left(2x-5\right)\left(x+2\right)+\left(x+2\right)^2=0\\ \Rightarrow\left(2x-5+x+2\right)^2=0\\ \Rightarrow3x-3=0\\ \Rightarrow x=1\\ b,\Rightarrow9-\left(x^2-5x\right)^2=9\\ \Rightarrow x^2-5x=0\\ \Rightarrow x\left(x-5\right)=0\Rightarrow\left[{}\begin{matrix}x=0\\x=5\end{matrix}\right.\)

\(a,=4x^2+3xy-y^2+4xy-4x^2=7xy-y^2\\ b,=x^2-9-x^3+3x+x^2-3=-x^3+2x^2+3x-12\\ c,=-2x^2+12x-18+5x^2+4x-1=3x^2+16x-19\\ d,=8x^3+1-3x^3+6x^2=5x^3+6x^2+1\\ e,=\left(3x^2+4x+15x+20\right):\left(3x+4\right)\\ =\left(3x+4\right)\left(x+5\right):\left(3x+4\right)\\ =x+5\\ f,=\left(x^3+4x^2-3x+3x^2+12x-9+3x+3\right):\left(x^2+4x-3\right)\\ =\left[\left(x^2+4x-3\right)\left(x+3\right)+3x+3\right]:\left(x^2+4x-3\right)\\ =x+3\left(dư.3x+3\right)\)

a: ta có: \(x^2+3x-\left(2x+6\right)=0\)

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

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

b: Ta có: \(5x+20-x^2-4x=0\)

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

\(\Leftrightarrow\left[{}\begin{matrix}x=-4\\x=5\end{matrix}\right.\)

\(a,\left(4x+1\right)\left(x-3\right)-\left(x-7\right)\left(4x-1\right)=15\\ \Leftrightarrow4x^2+x-12x-3-\left(4x^2-28x-x+7\right)-15=0\\ \Leftrightarrow4x^2-11x-3-4x^2+29x-7-15=0\\ \Leftrightarrow18x=25\\ \Leftrightarrow x=\dfrac{25}{18}\)

Vậy \(x=\dfrac{25}{18}\)

\(b,\left(x+1\right)\left(x^2-x+1\right)-x\left(x^2-3\right)=4\\ \Leftrightarrow x^3+1-x^3+3x-4=0\\ \Leftrightarrow3x-3=0\\ \Leftrightarrow x=1\)

Vậy \(x=1\)

\(c,\left(x-3\right)\left(x^2+3x+9\right)+x\left(5-x^2\right)-6x=0\\ \Leftrightarrow x^3-27+5x-x^3-6x=0\\ \Leftrightarrow-x-27=0\\ \Leftrightarrow x=-27\)

Vậy \(x=-27\)

\(d,\left(5x-1\right)\left(5x+1\right)=25x^2-7x+15\\ \Leftrightarrow25x^2-1-25x^2+7x-15=0\\ \Leftrightarrow7x-16=0\\ \Leftrightarrow x=\dfrac{16}{7}\)

Vậy \(x=\dfrac{16}{7}\)

=>x^4+4x^2+9-4x^3-6x^2+24x<x^4-4x^3-2x^2+15x-3

=>x^4-4x^3-2x^2+24x+9<x^4-4x^3-2x^2+15x-3

=>24x+9<15x-3

=>9x<-12

=>x<-4/3

1) \(\left(\dfrac{1}{2}x+3\right)\left(x^2-4x-6\right)\)

\(=\dfrac{1}{2}x^3-2x^2-3x+3x^2-12x-18\)

\(=\dfrac{1}{2}x^3+x^2-15x-18\)

2) \(\left(6x^2-9x+15\right)\left(\dfrac{2}{3}x+1\right)\)

\(=4x^3+6x^2-6x^2-9x+10x+15\)

\(=4x^3+x+15\)

3) Ta có: \(\left(3x^2-x+5\right)\left(x^3+5x-1\right)\)

\(=3x^5+15x^2-3x^2-x^4-5x^2+x+5x^3+25x-5\)

\(=3x^5-x^4+5x^3+10x^2+26x-5\)

4) Ta có: \(\left(x-1\right)\left(x+1\right)\left(x-2\right)\)

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

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

a: =>(2x-5x-1)(2x+5x+1)=0

=>(-3x-1)(7x+1)=0

=>x=-1/3 hoặc x=-1/7

b: =>(5x-5)^2-(x+2)^2=0

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

=>(4x-7)(6x-3)=0

=>x=1/2 hoặc x=7/4

c: =>(x^2+4x-1-x^2+3x-2)(x^2+4x-1+x^2-3x+2)=0

=>(7x-3)(2x^2+x+1)=0

=>7x-3=0

=>x=3/7