`a)x^2>4`

`<=>sqrtx^2>sqrt4`

`<=>|x|>2`

`<=>` \(\left[ \begin{array}{l}x>2\\x<-2\end{array} \right.\) 

`b)x^2<9`

`<=>\sqrtx^2<sqrt9`

`<=>|x|<3`

`<=>-3<x<3`

`c)(x-1)^2>=4`

`<=>\sqrt{(x-1)^2}>=sqrt4`

`<=>|x-1|>=2`

`<=>` \(\left[ \begin{array}{l}x-1 \ge 2\\x-1 \le -2\end{array} \right.\) 

`<=>` \(\left[ \begin{array}{l}x \ge 3\\x \le -1\end{array} \right.\) 

`d)(1-2x)^2<=0,09`

`<=>\sqrt{(1-2x)^2}<=sqrt{0,09}`

`<=>|2x-1|<=0,3`

`<=>-0,3<=2x-1<=0,3`

`<=>0,7<=2x<=1,3`

`<=>0,35<=x<=0,65`

`e)x^2+6x-7>0`

`<=>x^2-x+7x-7>0`

`<=>x(x-1)+7(x-1)>0`

`<=>(x-1)(x+7)>0`

TH1:

\(\left[ \begin{array}{l}x-1>0\\x+7>0\end{array} \right.\) 

`<=>` \(\left[ \begin{array}{l}x>1\\x>-7\end{array} \right.\) 

`<=>x>1`

TH2"

\(\left[ \begin{array}{l}x-1<0\\x+7<0\end{array} \right.\) 

`<=>` \(\left[ \begin{array}{l}x<1\\x<-7\end{array} \right.\) 

`<=>x<-7`

`f)x^2-x<2`

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

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

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

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

`<=>` \(\begin{cases}x-2<0\\x+1>0\\\end{cases}\)

`<=>` \(\begin{cases}x<2\\x>-1\\\end{cases}\)

`<=>-1<x<2`

a) x² > 4

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

b) \(x^2< 9\)

<=> \(-3< x< 3\)

c) \(\left(x-1\right)^2\ge4\)

<=> \(\left[{}\begin{matrix}x-1\ge2< =>x\ge3\\x-1\le-2< =>x\le-1\end{matrix}\right.\)

d) \(\left(1-2x\right)^2\le0,09\)

<=> \(-0,3\le1-2x\le0,3\)

<=> \(1,3\ge2x\ge0,7\)

<=> \(0,65\ge x\ge0,35\)

e) \(x^2+6x-7>0\)

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

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

f) \(x^2-x< 2\)

<=> \(x^2-x-2< 0\)

<=> \(\left(x-2\right)\left(x+1\right)< 0\)

<=> \(\left\{{}\begin{matrix}x+1>0< =>x>-1\\x-2< 0< =>x< 2\end{matrix}\right.\)

<=> -1 < x < 2

g) \(4x^2-12x\le\dfrac{-135}{16}\)

<=> \(64x^2-192x+135\le0\)

<=> (8x - 15)(8x - 9) \(\le0\)

<=> \(\left\{{}\begin{matrix}8x-15\le0< =>x\le\dfrac{15}{8}\\8x-9\ge0< =>x\ge\dfrac{9}{8}\end{matrix}\right.\)

<=> \(\dfrac{9}{8}\le x\le\dfrac{15}{8}\)

\(F=\sqrt{-3x^2-6x+2}\left(Đk:-1-\sqrt{\dfrac{5}{3}}\le x\le\sqrt{\dfrac{5}{3}}-1\right)\)

\(=\sqrt{-\left(3x^2+6x+3\right)+5}\)

\(=\sqrt{-3\left(x+1\right)^2+5}\)

Vì \(-\left(x+1\right)^2\le0\forall x\)

\(\Rightarrow F\le\sqrt{5}\)

\(MaxF=\sqrt{5}\Leftrightarrow x=-1\)

c: \(\Leftrightarrow\left(x-5\right)\left(x+1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=-1\end{matrix}\right.\)

Tìm min:

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

$=3[x^2+\frac{x}{3}+(\frac{1}{6})^2]-\frac{25}{12}$

$=3(x+\frac{1}{6})^2-\frac{25}{12}\geq \frac{-25}{12}$

Vậy $F_{\min}=\frac{-25}{12}$. Giá trị này đạt tại $x+\frac{1}{6}=0$
$\Leftrightarrow x=\frac{-1}{6}$

Tìm min

$G=4x^2+2x-1=(2x)^2+2.2x.\frac{1}{2}+(\frac{1}{2})^2-\frac{5}{4}$

$=(2x+\frac{1}{2})^2-\frac{5}{4}\geq 0-\frac{5}{4}=\frac{-5}{4}$ (do $(2x+\frac{1}{2})^2\geq 0$ với mọi $x$)

Vậy $G_{\min}=\frac{-5}{4}$. Giá trị này đạt tại $2x+\frac{1}{2}=0$

$\Leftrightarrow x=\frac{-1}{4}$

Tìm min

$H=5x^2-x+1=5(x^2-\frac{x}{5})+1$

$=5[x^2-\frac{x}{5}+(\frac{1}{10})^2]+\frac{19}{20}$

$=5(x-\frac{1}{10})^2+\frac{19}{20}\geq \frac{19}{20}$
Vậy $H_{\min}=\frac{19}{20}$. Giá trị này đạt tại $x-\frac{1}{10}=0$

$\Leftrightarrow x=\frac{1}{10}$

\(a,\Leftrightarrow9x^2=-36\Leftrightarrow x\in\varnothing\\ b,\Leftrightarrow3\left(x+4\right)-x\left(x+4\right)=0\\ \Leftrightarrow\left(3-x\right)\left(x+4\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=3\\x=-4\end{matrix}\right.\\ c,\Leftrightarrow2x^2-x-2x^2+3x+2=0\\ \Leftrightarrow2x=-2\Leftrightarrow x=-1\\ d,\Leftrightarrow\left(2x-3-2x\right)\left(2x-3+2x\right)=0\\ \Leftrightarrow-3\left(4x-3\right)=0\\ \Leftrightarrow x=\dfrac{3}{4}\\ e,\Leftrightarrow\dfrac{1}{3}x\left(x-9\right)=0\Leftrightarrow\left[{}\begin{matrix}x=0\\x=9\end{matrix}\right.\\ f,\Leftrightarrow x^2\left(x-1\right)-\left(x-1\right)=0\\ \Leftrightarrow\left(x^2-1\right)\left(x-1\right)=0\\ \Leftrightarrow\left(x-1\right)^2\left(x+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=1\\x=-1\end{matrix}\right.\)

\(4x^2-1=\left(2x-1\right)\left(2x+1\right)\)

\(x\left(x+y\right)-6x-6y=\left(x+y\right)\left(x-6\right)\)

\(x^2-2xy+y^2-z^2=\left(x-y-z\right)\left(x-y+z\right)\)

\(9x^2-\dfrac{1}{4}=\left(3x-\dfrac{1}{2}\right)\left(3x+\dfrac{1}{2}\right)\)

`#3107.101107`

a)

`x^2 + 6x + 10`

`= (x^2 + 2*x*3 + 3^2) + 1`

`= (x + 3)^2 + 1`

Vì `(x + 3)^2 \ge 0` `AA` `x`

`=> (x + 3)^2 + 1 \ge 1` `AA` `x`

Vậy, GTNN của bt là 1 khi `(x + 3)^2 = 0`

`<=> x + 3 = 0`

`<=> x = -3`

b)

`4x^2 - 4x + 5`

`= [(2x)^2 - 2*2x*1 + 1^2] + 4`

`= (2x - 1)^2 + 4`

Vì `(2x - 1)^2 \ge 0` `AA` `x`

`=> (2x - 1)^2 + 4 \ge 4` `AA` `x`

Vậy, GTNN của bt là `4` khi `(2x - 1)^2 = 0`

`<=> 2x - 1 = 0`

`<=> 2x = 1`

`<=> x = 1/2`

c)

`x^2 - 3x + 1`

`= (x^2 - 2*x*3/2 + 9/4) - 5/4`

`= (x - 3/2)^2 - 5/4`

Vì `(x - 3/2)^2 \ge 0` `AA` `x`

`=> (x - 3/2)^2 - 5/4 \ge -5/4` `AA` `x`

Vậy, GTNN của bt là `-5/4` khi `(x - 3/2)^2 = 0`

`<=> x - 3/2 = 0`

`<=> x = 3/2`

a.

\(1-4x^2=\left(1-2x\right)\left(1+2x\right)\)

b.

\(8-27x^3=\left(2\right)^3-\left(3x\right)^3=\left(2-3x\right)\left(4+6x+9x^2\right)\)

c.

\(27+27x+9x^2+x^3=x^3+3.x^2.3+3.3^2.x+3^3\)

\(=\left(x+3\right)^3\)

d.

\(2x^3+4x^2+2x=2x\left(x^2+2x+1\right)=2x\left(x+1\right)^2\)

e.

\(x^2-y^2-5x+5y=\left(x-y\right)\left(x+y\right)-5\left(x-y\right)\)

\(=\left(x-y\right)\left(x+y-5\right)\)

f.

\(x^2-6x+9-y^2=\left(x-3\right)^2-y^2=\left(x-3-y\right)\left(x-3+y\right)\)

g. 10x(x-y)-6y(y-x)

=10x(x-y)+6y(x-y)

=(x-y)(10x+6y)

h.x²-4x-5

=(x-5)(x+1)

i.x⁴-y⁴ = (x²-y²)(x²+y²)

B2.

a.5(x-2)=x-2

⇔5(x-2)-(x-2)=0

⇔4(x-2)=0

⇔x=2

b.3(x-5)=5-x

⇔3(x-5)+(x-5)=0

⇔4(x-5)=0

⇔x=5

c.(x+2)²-(x+2)(x-2)=0

⇔(x+2)[(x+2)-(x-2)]=0

⇔4(x+2)=0

⇔x=-2