a: \(2x^2-11x+21=3\cdot\sqrt[3]{4x-4}\)

=>\(2x^2-6x-5x+15=3\cdot\sqrt[3]{4x-4}-6\)

=>\(\left(x-3\right)\left(2x-5\right)=3\cdot\frac{4x-4-8}{\sqrt[3]{\left(4x-4\right)^2}+2\cdot\sqrt[3]{4x-4}+4}\)

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

=>\(\left(x-3\right)\left\lbrack\left(2x-5\right)-3\cdot\frac{4}{\sqrt[3]{\left(4x-4\right)^2}+2\cdot\sqrt[3]{4x-4}+4}\right\rbrack=0\)

=>x-3=0

=>x=3

1) \(\sqrt{5-2x}=6\left(đk:x\le\dfrac{5}{2}\right)\)

\(\Leftrightarrow5-2x=36\)

\(\Leftrightarrow2x=-31\Leftrightarrow x=-\dfrac{31}{2}\left(tm\right)\)

2) \(\sqrt{2-x}=\sqrt{x+1}\left(đk:2\ge x\ge-1\right)\)

\(\Leftrightarrow2-x=x+1\)

\(\Leftrightarrow2x=1\Leftrightarrow x=\dfrac{1}{2}\left(tm\right)\)

3) \(\Leftrightarrow\sqrt{\left(2x+1\right)^2}=6\)

\(\Leftrightarrow\left|2x+1\right|=6\)

\(\Leftrightarrow\left[{}\begin{matrix}2x+1=6\\2x+1=-6\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{2}\\x=-\dfrac{7}{2}\end{matrix}\right.\)

4) \(\sqrt{x^2-10x+25}=x-2\left(đk:x\ge2\right)\)

\(\Leftrightarrow\sqrt{\left(x-5\right)^2}=x-2\)

\(\Leftrightarrow\left|x-5\right|=x-2\)

\(\Leftrightarrow\left[{}\begin{matrix}x-5=x-2\left(x\ge5\right)\\x-5=2-x\left(2\le x< 5\right)\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}5=2\left(VLý\right)\\x=\dfrac{7}{2}\left(tm\right)\end{matrix}\right.\)

lamf nốt 4

c: ĐKXĐ: \(\begin{cases}x-2\ge0\\ x+2\ge0\\ x^2-4\ge0\end{cases}\)

=>x>=2 và \(x^2\ge4\)

=>x>=2

Ta có: \(\sqrt{x-2}-\sqrt{x+2}=2\cdot\sqrt{x^2-4}-2x+2\)

=>\(\sqrt{x-2}-\sqrt{x+2}+2=2\cdot\sqrt{x^2-4}-2x+4\)

=>\(\sqrt{x-2}-\frac{x+2-4}{\sqrt{x+2}+2}=2\cdot\sqrt{\left(x-2\right)\left(x+2\right)}-2\left(x-2\right)\)

=>\(\sqrt{x-2}\left(1-\frac{\sqrt{x-2}}{\sqrt{x+2}+2}\right)=2\sqrt{x-2}\left(\sqrt{x+2}-2\right)\)

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

=>\(\sqrt{x-2}=0\)

=>x-2=0

=>x=2(nhận)

Do vế trái dương nên pt chỉ có nghiệm khi \(x\ge\dfrac{3}{4}\), kết hợp điều kiện \(2x^4-3x^2+1\ge0\Rightarrow x\ge1\)

Khi đó:

\(4x-3=\sqrt{2x^4-3x^2+1}+\sqrt{2x^4-x^2}\ge\sqrt{2x^4-3x^2+1+2x^4-x^2}\)

\(\Rightarrow4x-3\ge\sqrt{4x^4-4x^2+1}\)

\(\Rightarrow4x-3\ge\left|2x^2-1\right|=2x^2-1\)

\(\Rightarrow2x^2-4x+2\le0\)

\(\Rightarrow2\left(x-1\right)^2\le0\)

\(\Rightarrow x=1\)

mong mọi người giải giúp em vs 

a: ĐKXĐ: \(x^2-1\ge0\)

=>x>=1 hoặc x<=-1

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

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

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

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

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

=>\(\sqrt{x-1}=0\)

=>x-1=0

=>x=1(nhận)