a) Ta có: \(x^2+3x-10=0\)

\(\Leftrightarrow x^2+5x-2x-10=0\)

\(\Leftrightarrow x\left(x+5\right)-2\left(x+5\right)=0\)

\(\Leftrightarrow\left(x+5\right)\left(x-2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x+5=0\\x-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-5\\x=2\end{matrix}\right.\)

Vậy: S={-5;2}

b) Ta có: \(3x^2-7x+1=0\)

\(\Leftrightarrow3\left(x^2-\dfrac{7}{3}x+\dfrac{1}{3}\right)=0\)

mà 3>0

nên \(x^2-\dfrac{7}{3}x+\dfrac{1}{3}=0\)

\(\Leftrightarrow x^2-2\cdot x\cdot\dfrac{7}{6}+\dfrac{49}{36}-\dfrac{37}{36}=0\)

\(\Leftrightarrow\left(x-\dfrac{7}{6}\right)^2=\dfrac{37}{36}\)

\(\Leftrightarrow\left[{}\begin{matrix}x-\dfrac{7}{6}=\dfrac{\sqrt{37}}{6}\\x-\dfrac{7}{6}=-\dfrac{\sqrt{37}}{6}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\sqrt{37}+7}{6}\\x=\dfrac{-\sqrt{37}+7}{6}\end{matrix}\right.\)

Vậy: \(S=\left\{\dfrac{\sqrt{37}+7}{6};\dfrac{-\sqrt{37}+7}{6}\right\}\)

c) Ta có: \(3x^2-7x+8=0\)

\(\Leftrightarrow3\left(x^2-\dfrac{7}{3}x+\dfrac{8}{3}\right)=0\)

mà 3>0

nên \(x^2-\dfrac{7}{3}x+\dfrac{8}{3}=0\)

\(\Leftrightarrow x^2-2\cdot x\cdot\dfrac{7}{6}+\dfrac{49}{36}+\dfrac{47}{36}=0\)

\(\Leftrightarrow\left(x-\dfrac{7}{6}\right)^2=-\dfrac{47}{36}\)(vô lý)

Vậy: \(x\in\varnothing\)

ko bt

20) -5-(x + 3) = 2 - 5x ⇔ -5 - x - 3 = 2 -5x ⇔ 4x = 10 ⇔ x = \(\frac{5}{2}\)

Vậy...

1) 16 - 8x = 0 ⇔ 8(2 - x) = 0⇔ 2 - x = 0 ⇔ x = 2

Vậy phương trình có nghiệm là x = 2

Ta có :

\(\dfrac{\left(3x^2+7x-10\right)}{x}=0\), ĐKXĐ \(x\ne0\)

\(\Leftrightarrow3x^2+7x-10=0\)

\(\Leftrightarrow3x^2+7x-3-7=0\)

\(\Leftrightarrow3\left(x^2-1\right)+7\left(x-1\right)=0\)

\(\Leftrightarrow3\left(x-1\right)\left(x+1\right)+7\left(x-1\right)=0\)

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

\(\Leftrightarrow\left[{}\begin{matrix}3x+10=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}3x=-10\\x=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{10}{3}\left(TM\right)\\x=1\left(TM\right)\end{matrix}\right.\)

Vậy \(x=-\dfrac{10}{3}\) hoặc x = 1

\(ĐKXĐ:x\ne0\)

\(\dfrac{3x^2+7x-10}{x}=0\)

\(\Leftrightarrow3x^2+7x-10=0\)

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

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

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

\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\3x+10=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-\dfrac{10}{3}\end{matrix}\right.\) ( t/m)

Vậy pt có tập nghiệm \(S=\left\{1;-\dfrac{10}{3}\right\}\)

1.

<=> \(\left[{}\begin{matrix}4-3x=0\\10-5x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{4}{3}\\x=2\end{matrix}\right.\)

2.

<=>\(\left[{}\begin{matrix}7-2x=0\\4+8x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{7}{2}\\x=-\dfrac{1}{2}\end{matrix}\right.\)

3.

<=>\(\left[{}\begin{matrix}9-7x=0\\11-3x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{9}{7}\\x=\dfrac{11}{3}\end{matrix}\right.\)

4.

<=>\(\left[{}\begin{matrix}7-14x=0\\x-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=2\end{matrix}\right.\)

5. 

<=>\(\left[{}\begin{matrix}\dfrac{7}{8}-2x=0\\3x+\dfrac{1}{3}=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{7}{16}\\x=-\dfrac{1}{9}\end{matrix}\right.\)

6,7. ko đủ điều kiện tìm

a)

a) $3x^2+12x-66=0$

=> 3(x + 2)² - 12 - 66 = 0

=> 3(x + 2)² - 78 = 0

=> 3(x + 2)² = 78

=> (x + 2)² = 26

=> x = \(\sqrt{26}-2\)

b)$9x^2-30x+225=0$

=> (3x - 5)² - 25 + 225 = 0

=> (3x - 5)² + 200 = 0

=> (3x - 5)² = -200

9x² - 30x + 225 không có ngiệmc)$x^2+3x-10=0$=> (x + 1,5)² - 2,25 - 10 = 0

=> (x + 1,5)² - 12,25 = 0

=> (x + 1,5)² = 12, 25

=> x + 1,5 = 3,5

=> x = 2

d)$3x^2-7x+1=0$=> 3(x - \(\dfrac{7}{6}\))² - \(\dfrac{49}{12}\) + 1 = 0

=> 3(x - \(\dfrac{7}{6}\))² - \(\dfrac{37}{12}\) = 0

=> 3(x - \(\dfrac{7}{6}\))² = \(\dfrac{37}{12}\)

=> (x - \(\dfrac{7}{6}\))² = \(\dfrac{37}{36}\)

=> x = \(\dfrac{\sqrt{37}}{6}+\dfrac{7}{6}=\dfrac{\sqrt{37}+7}{6}\)

e) $3x^2-7x+8=0$

=> 3(x - \(\dfrac{7}{6}\))² - \(\dfrac{49}{12}\)+ 8 = 0

=> 3(x - \(\dfrac{7}{6}\))² + \(\dfrac{47}{12}\) = 0

=> 3(x - \(\dfrac{7}{6}\))² = \(-\dfrac{47}{12}\)

KL : Không có ngiệm

a) 2x² - 3x - 2 = 0.

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

<=> 2x + 1 = 0 hoặc x - 2 = 0

<=> x = -1/2 hoặc x = 2

b) 3x² - 7x - 10 = 0.

<=> (x + 1)(3x - 10) = 0

<=> x = -1 hoặc x = 10/3

c) 2x² - 5x + 3 = 0.

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

<=> x = 1 hoặc x = 3/2

a)

\(3x^2+12x-66=0\)

\(\Leftrightarrow x^2+4x-22=0\)

\(\Leftrightarrow x^2+4x+4=26\Leftrightarrow (x+2)^2=26\)

\(\Rightarrow x+2=\pm \sqrt{26}\Rightarrow x=-2\pm \sqrt{26}\)

b)

\(9x^2-30x+225=0\)

\(\Leftrightarrow (3x)^2-2.3x.5+25+200=0\)

\(\Leftrightarrow (3x-5)^2=-200< 0\) (vô lý nên pt vô nghiệm)

c)

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

\(\Leftrightarrow x^2-2x+5x-10=0\)

\(\Leftrightarrow x(x-2)+5(x-2)=0\Leftrightarrow (x+5)(x-2)=0\)

\(\Rightarrow x=-5\) hoặc $x=2$

d)

$3x^2-7x+1=0$

$\Leftrightarrow 3(x^2-\frac{7}{3}x)+1=0$

$\Leftrightarrow 3(x^2-\frac{7}{3}x+\frac{7^2}{6^2})=\frac{37}{12}$

$\Leftrightarrow 3(x-\frac{7}{6})^2=\frac{37}{12}$
$\Leftrightarrow (x-\frac{7}{6})^2=\frac{37}{36}$

$\Rightarrow x-\frac{7}{6}=\frac{\pm \sqrt{37}}{6}$

$\Rightarrow x=\frac{7\pm \sqrt{37}}{6}$

e)

$3x^2+7x+2=0$

$\Leftrightarrow 3(x^2+\frac{7}{3}x+\frac{7^2}{6^2})=\frac{25}{12}$

$\Leftrightarrow 3(x+\frac{7}{6})^2=\frac{25}{12}$

$\Leftrightarrow (x+\frac{7}{6})^2=\frac{25}{36}$

$\Rightarrow x+\frac{7}{6}=\pm \frac{5}{6}$

$\Rightarrow x=\frac{-1}{3}$ hoặc $x=-2$

f)

$4x^2-12x+9=0$

$\Leftrightarrow (2x)^2-2.2x.3+3^2=0$

$\Leftrightarrow (2x-3)^2=0\Rightarrow 2x-3=0\Rightarrow x=\frac{3}{2}$

g) Trùng câu e

h)

$x^2-4x+1=0$

$\Leftrightarrow x^2-4x+4-3=0$

$\Leftrightarrow (x-2)^2=3\Rightarrow x-2=\pm \sqrt{3}$

$\Rightarrow x=2\pm \sqrt{3}$

i)

$2x^2-6x+1=0$

$\Leftrightarrow 2(x^2-3x+\frac{3^2}{2^2})=\frac{7}{2}$

$\Leftrightarrow 2(x-\frac{3}{2})^2=\frac{7}{2}$

$\Leftrightarrow (x-\frac{3}{2})^2=\frac{7}{4}$

$\Rightarrow x-\frac{3}{2}=\pm \frac{\sqrt{7}}{2}$

$\Rightarrow x=\frac{3\pm \sqrt{7}}{2}$

j)

$3x^2+4x-4=0$

$\Leftrightarrow 3x^2+6x-2x-4=0$

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

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

$\Rightarrow x+2=0$ hoặc $3x-2=0$

$\Rightarrow x=-2$ hoặc $x=\frac{2}{3}$