Trả lời:

a, \(\left(3x+1\right)\left(x-3\right)-x\left(3x-14\right)=15\)

\(\Leftrightarrow3x^2-9x+x-3-3x^2+14x=15\)

\(\Leftrightarrow6x-3=15\)

\(\Leftrightarrow6x=18\)

\(\Leftrightarrow x=3\)

Vậy x = 3 là nghiệm của pt.

b, \(\left(x-3\right)^2=9-x^2\)

\(\Leftrightarrow\left(x-3\right)^2-9+x^2=0\)

\(\Leftrightarrow\left(x-3\right)^2+\left(x^2-9\right)=0\)

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

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

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

\(\Leftrightarrow\orbr{\begin{cases}x-3=0\\2x=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=3\\x=0\end{cases}}}\)

Vậy x = 3; x = 0 là nghiệm của pt.

c, \(\left(2x-\frac{1}{2}\right)^2-\left(1-2x\right)^2=2\)

\(\Leftrightarrow4x^2-2x+\frac{1}{4}-\left(1-4x+4x^2\right)=2\)

\(\Leftrightarrow4x^2-2x+\frac{1}{4}-1+4x-4x^2=2\)

\(\Leftrightarrow2x-\frac{3}{4}=2\)

\(\Leftrightarrow2x=\frac{11}{4}\)

\(\Leftrightarrow x=\frac{11}{8}\)

Vậy x = 11/8 là nghiệm của pt.

d, \(4x^2+4x-3=0\)

\(\Leftrightarrow4x^2-2x+6x-3=0\)

\(\Leftrightarrow2x\left(2x-1\right)+3\left(2x-1\right)=0\)

\(\Leftrightarrow\left(2x-1\right)\left(2x+3\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}2x-1=0\\2x+3=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=\frac{1}{2}\\x=-\frac{3}{2}\end{cases}}}\)

Vậy x = 1/2; x = - 3/2 là nghiệm của pt.

giúp mk vs

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

\(\Leftrightarrow x^2-x^2-2x=6\)

<=> -2x = 6

<=> x = -3

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

\(\Leftrightarrow3x\left(x-2\right)-2x\left(x-2\right)=x^2-8\)

\(\Leftrightarrow\left(x-2\right)\left(3x-2x\right)=x^2-8\)

\(\Leftrightarrow\left(x-2\right)x=x^2-8\)

\(\Leftrightarrow x^2-2x=x^2-8\)

\(\Leftrightarrow2x=8\)

<=> x = 4 

a/ \(x^2-x\left(x+2\right)=6\)

<=> \(x^2-x^2-2x=6\)

<=> \(-2x=6\)

<=> \(x=-3\)

b/ \(3x\left(x-2\right)+2x\left(2-x\right)=x^2-8\)

<=> \(3x^2-6x+4x-2x^2=x^2-8\)

<=> \(3x^2-2x-2x^2-x^2+8=0\)

<=> \(-2x+8=0\)

<=> \(-2x=-8\)

<=> \(x=4\)

c/ \(3\left(5x-1\right)-x\left(x+1\right)+x^2=14\)

<=> \(15x-3-x^2-x+x^2=14\)

<=> \(14x-3=14\)

<=> \(-3=14-14x\)

<=> \(14\left(1-x\right)=-3\)

<=> \(1-x=\frac{-3}{14}\)

<=> \(-x=\frac{-3}{14}-1\)

<=> \(x=\frac{3}{14}+1\)

<=> \(x=\frac{17}{14}\)

giải giúp mk vs ạ

bn ơi mk rất mún giải hộ pạn nhưng mk k bít để giải xin lỗi pạn nhìu

k mk nhé

1: =>x^2+4x-21=0

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

=>x=3 hoặc x=-7

2: =>(2x-5-4)(2x-5+4)=0

=>(2x-9)(2x-1)=0

=>x=9/2 hoặc x=1/2

3: =>x^3-9x^2+27x-27-x^3+27+9(x^2+2x+1)=15

=>-9x^2+27x+9x^2+18x+9=15

=>18x=15-9-27=-21

=>x=-7/6

6: =>4x^2+4x+1-4x^2-16x-16=9

=>-12x-15=9

=>-12x=24

=>x=-2

7: =>x^2+6x+9-x^2-4x+32=1

=>2x+41=1

=>2x=-40

=>x=-20

a: Ta có: \(\left(x+2\right)\left(x^2-2x+4\right)-x\left(x^2+2\right)=15\)

\(\Leftrightarrow x^3+8-x^3-2x=15\)

\(\Leftrightarrow2x=-7\)

hay \(x=-\dfrac{7}{2}\)

b: Ta có: \(\left(x-2\right)^3-\left(x-4\right)\left(x^2+4x+16\right)+6\left(x+1\right)^2=49\)

\(\Leftrightarrow x^3-6x^2+12x-8-x^3+64+6\left(x+1\right)^2=49\)

\(\Leftrightarrow-6x^2+12x+56+6x^2+12x+6=49\)

\(\Leftrightarrow24x=-13\)

hay \(x=-\dfrac{13}{24}\)