a, ĐK: ​\(\left(x+1\right)\left(x^2+2x-1\right)\ge0\)​

\(x^2+5x+2=4\sqrt{x^3+3x^2+x-1}\)

\(\Leftrightarrow x^2+2x-1+3\left(x+1\right)-4\sqrt{\left(x+1\right)\left(x^2+2x-1\right)}=0\)

TH1: \(x\ge-1\)

\(pt\Leftrightarrow\left(\sqrt{x^2+2x-1}-\sqrt{x+1}\right)\left(\sqrt{x^2+2x-1}-3\sqrt{x+1}\right)=0\)

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

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

\(\Leftrightarrow\left[{}\begin{matrix}x^2+x-2=0\\x^2-7x-10=0\end{matrix}\right.\)

\(\Leftrightarrow...\)

TH2: \(x< -1\)

\(pt\Leftrightarrow\left(\sqrt{-x^2-2x+1}-\sqrt{-x-1}\right)\left(\sqrt{-x^2-2x+1}-3\sqrt{-x-1}\right)=0\)

\(\Leftrightarrow...\)

Bài này dài nên ... cho nhanh nha, đoạn sau dễ rồi

Đk: x>=0​

\(\Leftrightarrow\frac{x^2-1}{\sqrt[3]{\left(x^2+26\right)^2}+3\sqrt[3]{x^2+26}+9}+3\frac{x-1}{\sqrt{x}+1}+\frac{x-1}{\sqrt{x+3}+2}=0\)

\(\Leftrightarrow\left(x-1\right)\left(\frac{x+1}{\sqrt[3]{\left(x^2+26\right)^2}+3\sqrt[3]{x^2+26}+9}+\frac{3}{\sqrt{x}+1}+\frac{1}{\sqrt{x+3}+2}\right)=0\)

Với đk x>=0 ta có\(\frac{x+1}{\sqrt[3]{\left(x^2+26\right)^2}+3\sqrt[3]{x^2+26}+9}+\frac{3}{\sqrt{x}+1}+\frac{1}{\sqrt{x+3}+2}>0\)

pt <=> x-1=0<=>x=1 (tm)

ĐKXĐ: \(x\ge-2\)

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

Đặt \(\left\{{}\begin{matrix}\sqrt{x+2}=a\ge0\\\sqrt{x^2-2x+4}=b>0\end{matrix}\right.\)

\(\Rightarrow\sqrt{2}\left(2a^2+b^2\right)=5ab\)

\(\Leftrightarrow4a^2-5\sqrt{2}ab+2b^2=0\)

\(\Leftrightarrow\left(a-\sqrt{2}b\right)\left(4a-\sqrt{2}b\right)=0\)

Đến đây chắc bạn tự giải được

ĐKXĐ: 

Đặt {√x+2=a≥0√x2−2x+4=b>0{x+2=a≥0x2−2x+4=b>0