`a, 7x+2x=22-3x`

`<=>9x+3x=22`

`<=>12x=22`

`<=>x= 11/6`

Vậy pt có tập nghiệm `S={11/6}`

`b,8x-3=5x+12`

`<=>8x-5x=12+3`

`<=>3x=15`

`<=>x=5`

Vậy pt có tập nghiệm `S={5}`

`7/6 - 3/4`

`=14/12 - 9/12`

`=5/12`

`3a^2 -6ab + 3b^2 - 12c^2`

`=3(a^2 -2ab+b^2)-sqrt{12^2}c^2`

`=sqrt{3^2}(a-b)^2 - (sqrt{12}c)^2`

`=[sqrt{3}(a-b)]^2- (sqrt{12}c)^2`

`=(sqrt{3}a-sqrt{3}b)^2- (sqrt{12}c)^2`

`=(sqrt{3}a-sqrt{3}b-sqrt{12}c)(sqrt{3}a-sqrt{3}b+sqrt{12}c)`

`x^2 -6x+8=0`

`<=> x^2 -4x -2x+8=0`

`<=>x(x-4)-2(x-4)=0`

`<=>(x-2)(x-4)=0`

\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\x-4=0\end{matrix}\right.\\ \Leftrightarrow\Leftrightarrow\left[{}\begin{matrix}x=2\\x=4\end{matrix}\right.\)

`ĐKXĐ: 2x+3 > 0 <=> 2x> -3 <=> x > -3/2`

`ĐKXĐ: x-3 >0 <=> x> 0+3 <=> x>3`

\(\dfrac{x-1}{2}=\dfrac{y-2}{3}=\dfrac{z-3}{4}\Rightarrow\dfrac{2x-2}{4}=\dfrac{3y-6}{9}=\dfrac{7z-21}{28}\)

Áp dụng tính chất dãy tỉ số bằng nhau ta có:

\(\dfrac{2x-2}{4}=\dfrac{3y-6}{9}=\dfrac{7z-21}{28}=\dfrac{2x-2-3y+6+7z-21}{4-9+28}=\dfrac{\left(2x-3y+7z\right)-\left(2-6+21\right)}{23}=\dfrac{-29-17}{23}=\dfrac{-46}{23}=-2\)

\(\dfrac{x-1}{2}=-2\Rightarrow x-1=-2.2\Rightarrow x-1=-4\Rightarrow x=-3\\ =\dfrac{y-2}{3}=-2\Rightarrow y-2=-2.3\Rightarrow y-2=-6\Rightarrow y=-4\\ \dfrac{z-3}{4}=-2\Rightarrow z-3=-2.4\Rightarrow z-3=-8\Rightarrow z=-5\)

Ta có:

`x/15 = y/25 = z/35`

`=> (2x)/30 = y/25 = z/35`

Áp dụng tính chất dãy tỉ số bằng nhau ta có:
`(2x)/30 = y/25 = z/35 = (2x-y+z)/(30-25+35) = 35/40 = 7/8`

`(2x)/30 = 7/8 => x/15 = 7/8 => x =7/8 .15 = 105/8`

`y/25 = 7/8 => y= 7/8 .25 = 175/8`

`z/35 = 7/8 => z = 7/8 .35 = 245/8`