a) `4x^2+15x=25`
`<=>4x^2+15x-25=0`
`<=>(4x^2-5x)+(20x-25)=0`
`<=>x(4x-5)+5(4x-5)=0`
`<=>(4x-5)(x+5)=0`
`<=>4x-5=0` hoặc `x+5=0`
`<=>x=5/4` hoặc `x=-5`
b) `x^3+x^2=36`
`<=>x^3+x^2-36=0`
`<=>(x^3-3x^2)+(4x^2-12x)+(12x-36)=0`
`<=>x^2(x-3)+4x(x-3)+12(x-3)=0`
`<=>(x^2+4x+12)(x-3)=0`
`<=>x-3=0` (vì `x^2+4x+12=(x+2)^2+8>0` với mọi x)
`<=>x=3`
c) `x^3-4x=0`
`<=>x(x^2-4)=0`
`<=>x(x-2)(x+2)=0`
`<=>x=0` hoặc `x-2=0` hoặc `x+2=0`
`<=>x=0` hoặc `x=2` hoặc `x=-2`
d) `5x(x-1)=x-1`
`<=>5x(x-1)-(x-1)=0`
`<=>(5x-1)(x-1)=0`
`<=>5x-1=0` hoặc `x-1=0`
`<=>x=1/5` hoặc `x=1`
e: \(2\left(x+5\right)-x^2-5x=0\)
=>2(x+5)-x(x+5)=0
=>(x+5)(2-x)=0
=>\(\left[{}\begin{matrix}x+5=0\\2-x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-5\\x=2\end{matrix}\right.\)
f: \(6x^2+13x+5=0\)
=>\(6x^2+10x+3x+5=0\)
=>2x(3x+5)+(3x+5)=0
=>(3x+5)(2x+1)=0
=>\(\left[{}\begin{matrix}3x+5=0\\2x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{5}{3}\\x=-\dfrac{1}{2}\end{matrix}\right.\)
g: \(15x^2+11x-12=0\)
=>\(15x^2+20x-9x-12=0\)
=>\(5x\left(3x+4\right)-3\left(3x+4\right)=0\)
=>(3x+4)(5x-3)=0
=>\(\left[{}\begin{matrix}3x+4=0\\5x-3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{4}{3}\\x=\dfrac{3}{5}\end{matrix}\right.\)
h: \(5-6x+x^2=0\)
=>\(x^2-5x-x+5=0\)
=>x(x-5)-(x-5)=0
=>(x-5)(x-1)=0
=>\(\left[{}\begin{matrix}x-5=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\x=1\end{matrix}\right.\)
i: \(2x^3-16x=0\)
=>\(2x\left(x^2-8\right)=0\)
=>\(x\left(x^2-8\right)=0\)
=>\(\left[{}\begin{matrix}x=0\\x^2-8=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x^2=8\end{matrix}\right.\)
=>\(x\in\left\{0;2\sqrt{2};-2\sqrt{2}\right\}\)
