a) \(\left(x-3\right)^2+2x-6=0\)

\(\Leftrightarrow x^2-6x+9+2x-6=0\)

\(\Leftrightarrow x^2-4x+3=0\)

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

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

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

\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\x-3=0\end{matrix}\right.\)

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

b) \(\dfrac{x+3}{x-3}+\dfrac{48}{9-x^2}=\dfrac{x-3}{x+3}\) (ĐKXĐ: \(x\ne\pm3\))

\(\Leftrightarrow\dfrac{x+3}{x-3}-\dfrac{48}{\left(x+3\right)\left(x-3\right)}=\dfrac{x-3}{x+3}\)

\(\Leftrightarrow\dfrac{\left(x+3\right)^2}{\left(x+3\right)\left(x-3\right)}-\dfrac{48}{\left(x+3\right)\left(x-3\right)}=\dfrac{\left(x-3\right)^2}{\left(x+3\right)\left(x-3\right)}\)

\(\Leftrightarrow x^2+6x+9-48=x^2-6x+9\)

\(\Leftrightarrow x^2-x^2+6x+6x+9-9-48=0\)

\(\Leftrightarrow12x-48=0\)

\(\Leftrightarrow12x=48\)

\(\Leftrightarrow x=\dfrac{48}{12}\)

\(\Leftrightarrow x=4\left(tm\right)\)

a: (x-3)^2+2x-6=0

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

=>(x-3)(x-3+2)=0

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

=>x=3 hoặc x=1

b:

ĐKXĐ: x<>3; x<>-3

 \(\dfrac{x+3}{x-3}+\dfrac{48}{9-x^2}=\dfrac{x-3}{x+3}\)

=>\(\dfrac{\left(x+3\right)^2}{\left(x-3\right)\left(x+3\right)}-\dfrac{48}{\left(x-3\right)\cdot\left(x+3\right)}=\dfrac{\left(x-3\right)^2}{\left(x+3\right)^2}\)

=>(x+3)^2-48=(x-3)^2

=>x^2+6x+9-48=x^2-6x+9

=>6x-39=-6x+9

=>12x=48

=>x=4(nhận)

\(a,\left(x-3\right)^2-2x+6=0\\ \Leftrightarrow x^2-6x+9-2x+6=0\\ \Leftrightarrow x^2-8x+15=0\\ \Leftrightarrow x^2-3x-5x+15=0\\ \Leftrightarrow x\left(x-3\right)-5\left(x-3\right)=0\\ \Leftrightarrow\left(x-5\right)\left(x-3\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x-5=0\\x-3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\x=3\end{matrix}\right.\\ Vậy:S=\left\{5;3\right\}\\ b,\dfrac{x+3}{x-3}+\dfrac{48}{9-x^2}=\dfrac{x-3}{x+3}\left(ĐKXĐ:x\ne\pm3\right)\\ \Leftrightarrow\dfrac{\left(x+3\right)^2-48-\left(x-3\right)^2}{x^2-9}=0\\ \Leftrightarrow\left[\left(x+3-x+3\right)\left(x+3+x-3\right)\right]-48=0\\ \Leftrightarrow6.2x-48=0\\ \Leftrightarrow12x=48\\ \Leftrightarrow x=4\left(TM\right)\\ Vậy:S=\left\{4\right\}\)

a: \(\dfrac{x}{2}+\dfrac{1-x}{3}>0\)

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

=>3x+2-2x>0

=>x+2>0

=>x>-2

b: (x-9)^2-x(x+9)<0

=>x^2-18x+81-x^2-9x<0

=>-27x+81<0

=>-27x<-81

=>x>3

S = (2+2^2)+(2^3+2^4)+...+(2^99+2^100)

= 2(1+2)+2^3(1+2)+...+2^99(1+2)

= 2.3+2^3 .3+...+2^99 .3

=3(2+2^3+...+2^99) chia hết cho 3

Hay S là bội của 3

8,75

5/10

bằng 8,75

=14

14 ☺

`@` `\text {Ans}`

`\downarrow`

`5^2 \times 2 - 3^2 \times 4`

`= 25 \times 2 - 9 \times 4`

`= 50 - 36`

`= 14`

a: \(P\left(x\right)=3x^2-4x+7\)

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

b: \(P\left(x\right)-Q\left(x\right)=3x^2-4x+7-5x^3+x^2-4x+3\)

\(=-5x^3+4x^2-8x+10\)