2:

a: =>2x^2-4x-2=x^2-x-2

=>x^2-3x=0

=>x=0(loại) hoặc x=3

b: =>(x+1)(x+4)<0

=>-4<x<-1

d: =>x^2-2x-7=-x^2+6x-4

=>2x^2-8x-3=0

=>\(x=\dfrac{4\pm\sqrt{22}}{2}\)

\(\sqrt{x+8}-\sqrt{5x+2}+2=0\)             

<=> \(\sqrt{x+8}=\sqrt{5x+2}-2\)

<=> x + 8 = \(\left(\sqrt{5x+2}-2\right)^2\)

<=> x + 8 = \(\left(\sqrt{5x+2}\right)^2-4\sqrt{5x+2}+4\)

<=> x + 8 = 5x + 2 - \(4\sqrt{5x+2}+4\)

<=> \(4\sqrt{5x+2}=5x+2+4-x-8\)

<=> \(4\sqrt{5x+2}=4x-2\)

<=> \(4\sqrt{5x+2}=2\left(2x-1\right)\)

<=> \(\sqrt{5x+2}=\dfrac{2\left(2x-1\right)}{4}\)

<=> \(\sqrt{5x+2}=\dfrac{2x-1}{2}\)

<=> 5x + 2 = \(\dfrac{\left(2x-1\right)^2}{4}\)

<=> x = \(\dfrac{\dfrac{\left(2x-1\right)^2}{4}-2}{5}\)

<=> x = -0,278.....

Hung nguyen, Trần Thanh Phương, Sky SơnTùng, @tth_new, @Nguyễn Việt Lâm, @Akai Haruma, @No choice teen

help me, pleaseee

Cần gấp lắm ạ!

\(ĐK:x\ge-4\\ \Leftrightarrow\sqrt{x+8}=\sqrt{5x+20}-2\\ \Leftrightarrow x+8=5x+20+4-4\sqrt{5x+20}\\ \Leftrightarrow4\sqrt{5x+20}=4x+16\\ \Leftrightarrow\left(\sqrt{5x+20}\right)^2=\left[4\left(x+4\right)\right]^2\\ \Leftrightarrow5x+20=16\left(x^2+8x+64\right)\\ \Leftrightarrow5x+20=16x^2+128x+1024\\ \Leftrightarrow16x^2+123x+1004=0\\ \Leftrightarrow\left(16x^2+2\cdot4x\cdot\dfrac{123}{8}+\dfrac{15129}{64}\right)+\dfrac{49127}{64}=0\\ \Leftrightarrow\left(4x+\dfrac{123}{8}\right)^2+\dfrac{49127}{64}=0\Leftrightarrow x\in\varnothing\)

a: ĐKXĐ: \(x\in R\)

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

=>|2x+3|=5

=>\(\left[{}\begin{matrix}2x+3=5\\2x+3=-5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=2\\2x=-8\end{matrix}\right.\)

=>\(\left[{}\begin{matrix}x=1\left(nhận\right)\\x=-4\left(nhận\right)\end{matrix}\right.\)

b: ĐKXĐ: \(x\in R\)

\(\sqrt{9\left(x-2\right)^2}=18\)

=>\(\sqrt{9}\cdot\sqrt{\left(x-2\right)^2}=18\)

=>\(3\cdot\left|x-2\right|=18\)

=>\(\left|x-2\right|=6\)

=>\(\left[{}\begin{matrix}x-2=6\\x-2=-6\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=8\left(nhận\right)\\x=-4\left(nhận\right)\end{matrix}\right.\)
c: ĐKXĐ: x>=2

\(\sqrt{9x-18}-\sqrt{4x-8}+3\sqrt{x-2}=40\)

=>\(3\sqrt{x-2}-2\sqrt{x-2}+3\sqrt{x-2}=40\)

=>\(4\sqrt{x-2}=40\)

=>\(\sqrt{x-2}=10\)

=>x-2=100

=>x=102(nhận)

d: ĐKXĐ: \(x\in R\)

\(\sqrt{4\left(x-3\right)^2}=8\)

=>\(\sqrt{\left(2x-6\right)^2}=8\)

=>|2x-6|=8

=>\(\left[{}\begin{matrix}2x-6=8\\2x-6=-8\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=14\\2x=-2\end{matrix}\right.\)

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

e: ĐKXĐ: \(x\in R\)

\(\sqrt{4x^2+12x+9}=5\)

=>\(\sqrt{\left(2x\right)^2+2\cdot2x\cdot3+3^2}=5\)

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

=>|2x+3|=5

=>\(\left[{}\begin{matrix}2x+3=5\\2x+3=-5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=2\\2x=-8\end{matrix}\right.\)

=>\(\left[{}\begin{matrix}x=1\left(nhận\right)\\x=-4\left(nhận\right)\end{matrix}\right.\)

f: ĐKXĐ:x>=6/5

\(\sqrt{5x-6}-3=0\)

=>\(\sqrt{5x-6}=3\)

=>\(5x-6=3^2=9\)

=>5x=6+9=15

=>x=15/5=3(nhận)

`a)sqrt{5x-2}=3(x>=2/5)`

`<=>5x-2=9`

`<=>5x=11`

`<=>x=11/5(tm)`

`b)sqrt{x^2-4x+4}-5=0`

`<=>\sqrt{(x-2)^2}=5`

`<=>|x-2|=5`

`<=>` \(\left[ \begin{array}{l}x-2=5\\x-2=-5\end{array} \right.\) 

`<=>` \(\left[ \begin{array}{l}x=7\\x=-3\end{array} \right.\) 

`c)3sqrt{4x+8}-sqrt{9x+18}+9sqrt{(x+2)/9}=sqrt{72}(x>=-2)`

`<=>6sqrt{x+2}-3sqrt{x+2}+3sqrt{x+2}=sqrt{72}`

`<=>6sqrt{x+2}=6sqrt2`

`<=>sqrt{x+2}=sqrt2`

`<=>x+2=2`

`<=>x=0(tm)`

\(a,ĐK:x\ge\dfrac{2}{5}\)

\(\Leftrightarrow5x-2=9\)

\(\Leftrightarrow5x=11\)

\(\Leftrightarrow x=\dfrac{11}{5}\)

\(b,\)

\(\Leftrightarrow x^2-5x+4=25\)

\(\Leftrightarrow x^2-5x-21=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5+\sqrt{109}}{2}\\x=\dfrac{5-\sqrt{109}}{2}\end{matrix}\right.\)

\(c,\)

\(\Leftrightarrow6\sqrt{x+2}-3\sqrt{x+2}+9\cdot\sqrt{\dfrac{x+2}{9}}=6\sqrt{2}\)

\(\Leftrightarrow2\sqrt{x+2}-\sqrt{x+2}+3\cdot\sqrt{\dfrac{x+2}{9}}=2\sqrt{2}\)

Đặt \(\sqrt{x+2}=a\) ta có (1)

\(2a-a+3\cdot\dfrac{a}{\sqrt{9}}=2\sqrt{2}\)

\(\Leftrightarrow a+3\cdot\dfrac{a}{3}=2\sqrt{2}\)

\(\Leftrightarrow2a=2\sqrt{2}\)

\(\Leftrightarrow a=\sqrt{2}\)

Thay \(a=\sqrt{2}\) vào (1) ta có

\(\sqrt{x+2}=\sqrt{2}\)

\(\Leftrightarrow x+2=2\)

\(\Leftrightarrow x=0\)

Bài 2:
ĐKXĐ: $6\geq x\geq \frac{-1}{3}$
PT $\Leftrightarrow (\sqrt{3x+1}-4)+(1-\sqrt{6-x})+(3x^2-14x-5)=0$

$\Leftrightarrow \frac{3(x-5)}{\sqrt{3x+1}+4}+\frac{x-5}{\sqrt{6-x}+1}+(3x+1)(x-5)=0$
$\Leftrightarrow (x-5)\left[\frac{3}{\sqrt{3x+1}+4}+\frac{1}{\sqrt{6-x}+1}+(3x+1)\right]=0$

Với $x$ thuộc đkxđ, dễ thấy biểu thức trong ngoặc vuông $>0$

$\Rightarrow x-5=0$

$\Leftrightarrow x=5$

Bài 3:

PT $3x=\sqrt{x^2+12}-\sqrt{x^2+5}+5>0$

$\Rightarrow x>0$

Lại có:

PT $\Leftrightarrow \sqrt{x^2+12}-4=3(x-2)+(\sqrt{x^2+5}-3)$

$\Leftrightarrow \frac{x^2-4}{\sqrt{x^2+12}+4}=3(x-2)+\frac{x^2-4}{\sqrt{x^2+5}+3}$

$\Leftrightarrow (x-2)\left[\frac{x+2}{\sqrt{x^2+12}+4}-3-\frac{x+2}{\sqrt{x^2+5}+3}\right]=0$

Với $x>0$, dễ thấy:
$\frac{x+2}{\sqrt{x^2+5}+3}+3>\frac{x+2}{\sqrt{x^2+12}+4}$ nên biểu thức trong ngoặc vuông âm.

Do đó $x-2=0\Leftrightarrow x=2$ (tm)

Bài 1:

Đặt $\sqrt[3]{3x-2}=a; \sqrt{6-5x}=b$ với $b\geq 0$. Khi đó pt trở thành:
\(\left\{\begin{matrix} 2a+3b=8\\ 5a^3+3b^2=8\end{matrix}\right.\Rightarrow 5a^3+3(\frac{8-2a}{3})^2=8\)

\(\Leftrightarrow 15a^3+(8-2a)^2=24\)

\(\Leftrightarrow 15a^3+4a^2-32a+40=0\)

\(\Leftrightarrow 15a^2(a+2)-26a(a+2)+20(a+2)=0\)

$\Leftrightarrow (a+2)(15a^2-26a+20)=0$

Dễ thấy $15a^2-26a+20>0$ nên $a+2=0$

$\Leftrightarrow a=-2$
$\Rightarrow b=4$

$\Rightarrow x=-2$