a: =>14x+20+5=6x-9-9x

=>14x+25=-3x-9

=>17x=-34

=>x=-2

b: =>\(2x^2-30x+2x-30=2x^2+10x-10x-50\)

=>-28x-30=-50

=>-28x=-20

=>x=20/28=5/7

c: =>2x+x^3-x=x^3+1

=>x=1

d: =>x^3-3x^2+3x-1-x(x^2+2x+1)=10x-2x^2-11x-22

=>x^3-3x^2+3x-1-x^3-2x^2-x=-2x^2-x-22

=>-5x^2+2x-1+2x^2+x+22=0

=>-3x^2+3x+21=0

=>x^2-x-7=0

=>\(x=\dfrac{1\pm\sqrt{29}}{2}\)

tìm x nha

c, \(3x^2-7x+10=0\)

\(\Leftrightarrow3x^2+3x-10x+10=0\)

\(\Leftrightarrow3x\left(x+1\right)-10\left(x+1\right)=0\)

\(\Leftrightarrow\left(x+1\right)\left(3x-10\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=\dfrac{10}{3}\end{matrix}\right.\)

d, \(2x\left(x-10\right)-x+10=0\)

\(\Leftrightarrow2x\left(x-10\right)-\left(x-10\right)=0\)

\(\Leftrightarrow\left(x-10\right)\left(2x-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=10\\x=\dfrac{1}{2}\end{matrix}\right.\)

a: Ta có: \(x\left(2x-3\right)-\left(2x-1\right)\left(x+5\right)=17\)

\(\Leftrightarrow2x^2-3x-2x^2-10x+x+5=17\)

\(\Leftrightarrow-12x=12\)

hay x=-1

Máy bài này khá dễ chỉ cần suy nghĩ tí là làm được.

Đặt `2x^2-x=a(a>=-1/8)`

`pt<=>1/(a+1)+3/(a+3)=10/(a+7)`

`<=>(a+3)(a+7)+3(a+1)(a+7)=10(a+1)(a+3)`

`<=>a^2+10a+21+3(a^2+8a+7)=10(a^2+4a+3)`

`<=>a^2+3a^2+10a+24a+21+21=10a^2+40a+30`

`<=>4a^2+34a+42=10a^2+40a+30`

`<=>6a^2+6a-12=0`

`<=>a^2+a-2=0`

`a+b+c=0`

`=>a_1=1,a_2=-2(l)`

`a=1=>2x^2-x=1`

`=>2x^2-x-1=0`

`a+b+c=0`

`=>x_1=1,x_1=-1/2`

Vậy `S={1,-1/2}`

Đặt \(2x^2-x+1=a\left(a\ge\dfrac{7}{8}\right)\)

PTTT : \(\dfrac{1}{a}+\dfrac{3}{a+2}=\dfrac{10}{a+6}\)

\(\Leftrightarrow\left(a+2\right)\left(a+6\right)+3a\left(a+6\right)=10a\left(a+2\right)\)

\(\Leftrightarrow a^2+2a+6a+12+3a^2+18a=10a^2+20a\)

\(\Leftrightarrow-6a^2+6a+12=0\)

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

\(\Leftrightarrow a=2\)

-Thay lại a = 2 ta được : \(2x^2-x-1=0\)

<=> \(\left[{}\begin{matrix}x=1\\x=-\dfrac{1}{2}\end{matrix}\right.\)

Vậy ...

đk: \(_{x+1\ne0\Leftrightarrow x\ne-1}\)\(\dfrac{1-x}{x+1}+3=\dfrac{2x-3}{x+1}\Leftrightarrow\dfrac{1-x}{x+1}+\dfrac{3\left(x+1\right)}{x+1}=\dfrac{2x+3}{x-1}\Leftrightarrow1-x+3x+3-2x-3=0\Leftrightarrow-2x+1=0\Leftrightarrow-2x=-1\Leftrightarrow x=0,5\)

\(a)PT\Leftrightarrow4x^2-9-4x^2+20x+3x=0.\\ \Leftrightarrow23x=9.\\ \Leftrightarrow x=\dfrac{9}{23}.\\ b)PT\Leftrightarrow\left(2x+1\right)\left(4x-3\right)-\left(2x+1\right)\left(2x-1\right)=0.\\\Leftrightarrow\left(2x+1\right)\left(4x-3-2x+1\right)=0.\\ \Leftrightarrow\left(2x+1\right)\left(2x-2\right)=0.\\ \Leftrightarrow\left(2x+1\right)\left(x-1\right)=0. \)

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