b.

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

\(\Leftrightarrow x^4+2x^2-4+x\sqrt{2x^2+4x}=0\)

Đặt \(x\sqrt{2x^2+4x}=t\Rightarrow t^2=x^2\left(2x^2+4x\right)=2\left(x^4+2x^2\right)\)

Pt trở thành:

\(\dfrac{t^2}{2}-4+t=0\)

\(\Leftrightarrow t^2+2t-8=0\Rightarrow\left[{}\begin{matrix}t=2\\t=-4\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x\sqrt{2x^2+4x}=2\left(x>0\right)\\x\sqrt{2x^2+4x}=-4\left(x< 0\right)\end{matrix}\right.\)

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

\(\Leftrightarrow\left[{}\begin{matrix}x=\sqrt{\sqrt{3}-1}\\x=-\sqrt{2}\end{matrix}\right.\)

a.

ĐKXĐ: \(x\ne0\)

\(\Leftrightarrow\dfrac{9}{x^2}+2+\dfrac{2x}{\sqrt{2x^2+9}}=3\)

\(\Leftrightarrow\dfrac{2x^2+9}{x^2}+\dfrac{2x}{\sqrt{2x^2+9}}=3\)

Đặt \(\dfrac{x}{\sqrt{2x^2+9}}=t\Rightarrow\dfrac{2x^2+9}{x^2}=\dfrac{1}{t^2}\)

Pt trở thành:

\(\dfrac{1}{t^2}+2t=3\)

\(\Rightarrow2t^3-3t^2+1=0\)

\(\Leftrightarrow\left(t-1\right)^2\left(2t+1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}t=1\\t=-\dfrac{1}{2}\end{matrix}\right.\)

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

\(\Leftrightarrow\left[{}\begin{matrix}x^2=2x^2+9\left(vô-nghiệm\right)\\4x^2=2x^2+9\left(x< 0\right)\end{matrix}\right.\)

\(\Leftrightarrow x=-\dfrac{3\sqrt{2}}{2}\)

Kiểm tra lại vế trái đề bài câu b

a: |x+9|=2

=>x+9=2 hoặc x+9=-2

=>x=-7 hoặc x=-11

b: |2x-3|=x-3

\(\Leftrightarrow\left\{{}\begin{matrix}x>=3\\\left(2x-3-x+3\right)\left(2x-3+x-3\right)=0\end{matrix}\right.\Leftrightarrow x=3\)

refer

1: \(\Leftrightarrow\left(x-4\right)^2+14=-9\left(x-4\right)\)

\(\Leftrightarrow x^2-8x+16+14+9x-36=0\)

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

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

=>x=-3(nhận) hoặc x=2(nhận)

2: \(\Leftrightarrow\left(8x+1\right)\left(2x-1\right)-2x\left(2x+1\right)-12x^2+9=0\)

\(\Leftrightarrow16x^2-8x+2x-1-4x^2-2x-12x^2+9=0\)

=>-8x+8=0

hay x=1(nhận)

c: \(\dfrac{1}{2\left(x-3\right)}-\dfrac{3x-5}{\left(x-3\right)\left(x-1\right)}=\dfrac{1}{2}\)

\(\Leftrightarrow x-1-2\left(3x-5\right)=\left(x-3\right)\left(x-1\right)\)

\(\Leftrightarrow x^2-4x+3=x-1-6x+10=-5x+9\)

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

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

=>x=-3(nhận) hoặc x=2(nhận)

a.

ĐKXĐ: \(x^2+2x-1\ge0\)

\(x^2+2x-1+2\left(x-1\right)\sqrt{x^2+2x-1}-4x=0\)

Đặt \(\sqrt{x^2+2x-1}=t\ge0\)

\(\Rightarrow t^2+2\left(x-1\right)t-4x=0\)

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

\(\Rightarrow\left[{}\begin{matrix}t=1-x+x+1=2\\t=1-x-x-1=-2x\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}\sqrt{x^2+2x-1}=2\\\sqrt{x^2+2x-1}=-2x\left(x\le0\right)\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x^2+2x-5=0\\3x^2-2x+1=0\left(vn\right)\end{matrix}\right.\)

\(\Rightarrow x=-1\pm\sqrt{6}\)

b.

ĐKXĐ: \(x\ge\dfrac{1}{5}\)

\(2x^2+x-3+2x-\sqrt{5x-1}+2-\sqrt[3]{9-x}=0\)

\(\Leftrightarrow\left(x-1\right)\left(2x+3\right)+\dfrac{\left(x-1\right)\left(4x-1\right)}{2x+\sqrt[]{5x-1}}+\dfrac{x-1}{4+2\sqrt[3]{9-x}+\sqrt[3]{\left(9-x\right)^2}}=0\)

\(\Leftrightarrow\left(x-1\right)\left(2x+3+\dfrac{4x-1}{2x+\sqrt[]{5x-1}}+\dfrac{1}{4+2\sqrt[3]{9-x}+\sqrt[3]{\left(9-x\right)^2}}\right)=0\)

\(\Leftrightarrow x=1\) (ngoặc đằng sau luôn dương)

\(a,\left(2x-3\right)^2=\left(x+1\right)^2\\ \Leftrightarrow\left(2x-3\right)^2-\left(x+1\right)^2=0\\ \Leftrightarrow\left(2x-3+x+1\right)\left(2x-3-x-1\right)=0\\ \Leftrightarrow\left(3x-2\right)\left(x-4\right)\\ \Leftrightarrow\left[{}\begin{matrix}3x-2=0\\x-4=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}3x=2\\x=4\end{matrix}\right. \\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{2}{3}\\x=4\end{matrix}\right.\)

Vậy \(x\in\left\{\dfrac{2}{3};4\right\}\)

\(b,x^2-6x+9=9\left(x-1\right)^2\\ \Leftrightarrow\left(x-3\right)^2=9\left(x-1\right)^2\\ \Leftrightarrow\left(x-3\right)^2-9\left(x-1\right)^2=0\\ \Leftrightarrow\left(x-3\right)^2-3^2\left(x-1\right)^2=0\\ \Leftrightarrow\left(x-3\right)^2-\left[3\left(x-1\right)\right]^2=0\\ \Leftrightarrow\left(x-3\right)^2-\left(3x-3\right)^2=0\\ \Leftrightarrow\left(x-3+3x-3\right)\left(x-3-3x+3\right)=0\\ \Leftrightarrow-2x\left(4x-6\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}-2x=0\\4x-6=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\4x=6\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{3}{2}\end{matrix}\right.\)

Vậy \(x\in\left\{0;\dfrac{3}{2}\right\}\)

x-1 + x-3 =1 <=> 2x -4=1 tu giai not

\(\sqrt{x^2-x+1}+\sqrt{x^2-9x+9}=2x\)

=>\(\sqrt{x^2-x+1}-x+\sqrt{x^2-9x+9}-x=0\)

=>\(\dfrac{x^2-x+1-x^2}{\sqrt{x^2-x+1}+x}+\dfrac{x^2-9x+9-x^2}{\sqrt{x^2-9x+9}+x}=0\)

=>\(\left(-x+1\right)\left(\dfrac{1}{\sqrt{x^2-x+1}+x}+\dfrac{9}{\sqrt{x^2-9x+9}+x}\right)=0\)

=>-x+1=0

=>x=1

1. 4x-12=0

<=>4x=12

<=>x=3

2.  x.(x+1)-(x+2)(x+3)=7

<=>x²+x-x²-3x-2x-6=7

<=>x²-x²+x-2x-3x=7+6

<=>-4x=13

<=>x=\(-\dfrac{13}{4}\)

3.   7+2x=22-3x

<=>2x+3x=22-7

<=>5x=15

<=>x=3

4.  (x-1)-(2x-1)=9-x

<=>x-1-2x+1=9-x

<=>x-2x+x=9+1-1

<=>0x=9

vô nghiệm