ĐKXĐ: \(x\ge1;x\le-3;x=-1\)

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

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

\(\left(1\right)\Leftrightarrow x+1=0\Rightarrow x=-1\)

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

\(\Leftrightarrow2x+6=x-1+4\sqrt{\left(x-1\right)\left(x+1\right)}+4x+4\)

\(\Leftrightarrow4\sqrt{x^2-1}=3-3x\) \(\Leftrightarrow\left\{{}\begin{matrix}3-3x\ge0\\16\left(x^2-1\right)=\left(3-3x\right)^2\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\le1\\7x^2+18x-25=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=1\\x=\dfrac{-25}{7}\end{matrix}\right.\)

Vậy pt có 3 nghiệm: \(x=-1;1;\dfrac{-25}{7}\)

ĐKXĐ : \(x\ge\sqrt{3}\)

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

\(\Leftrightarrow3x+\sqrt{3}-2\sqrt{\left(3x+\sqrt{3}\right)\left(x-\sqrt{3}\right)}+x-\sqrt{3}=4x\)

\(\Leftrightarrow2\sqrt{\left(3x+\sqrt{3}\right)\left(x-\sqrt{3}\right)}=0\)

\(\Leftrightarrow\orbr{\begin{cases}3x+\sqrt{3}=0\\x-\sqrt{3}=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=\frac{-\sqrt{3}}{3}\left(ktm\right)\\x=\sqrt{3}\left(tm\right)\end{cases}}}\)

Vậy phương trình có nghiệm duy nhất là \(x=\sqrt{3}\)

đk: \(x\ge\sqrt{3}\)

Ta có: \(\sqrt{3x+\sqrt{3}}-\sqrt{x-\sqrt{3}}=2\sqrt{x}\)

\(\Leftrightarrow3x+\sqrt{3}-2\sqrt{\left(3x+\sqrt{3}\right)\left(x-\sqrt{3}\right)}+x-\sqrt{3}=4x\)

\(\Leftrightarrow2\sqrt{\left(3x+\sqrt{3}\right)\left(x-\sqrt{3}\right)}=0\)

\(\Leftrightarrow\left(3x+\sqrt{3}\right)\left(x-\sqrt{3}\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}3x+\sqrt{3}=0\\x-\sqrt{3}=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-\frac{\sqrt{3}}{3}\left(ktm\right)\\x=\sqrt{3}\left(tm\right)\end{cases}}\)

Vậy \(x=\sqrt{3}\)

ĐKXĐ: \(x\ge\sqrt{3}\)

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

+) Xét \(2\sqrt{x}=\sqrt{x-\sqrt{3}}\Rightarrow4x=x-3\Leftrightarrow x=-1\)---> Không thỏa ĐKXĐ

Vậy \(2\sqrt{x}-\sqrt{x-\sqrt{3}}\ne0\)---> Ta dùng lượng liên hiệp:

\(\sqrt{3x+\sqrt{3}}=\frac{\left(2\sqrt{x}+\sqrt{x-\sqrt{3}}\right)\left(2\sqrt{x}-\sqrt{x-\sqrt{3}}\right)}{2\sqrt{x}-\sqrt{x-\sqrt{3}}}=\frac{4x-\left(x-\sqrt{3}\right)}{2\sqrt{x}-\sqrt{x-\sqrt{3}}}\)

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

Vì \(x\ge\sqrt{3}\Rightarrow\sqrt{3x+\sqrt{3}}>0\Rightarrow1-\frac{\sqrt{3x+\sqrt{3}}}{2\sqrt{x}-\sqrt{x-\sqrt{3}}}=0\)

\(\Leftrightarrow2\sqrt{x}-\sqrt{x-\sqrt{3}}=\sqrt{3x+\sqrt{3}}\Rightarrow3x+\sqrt{3}-4\sqrt{x}.\sqrt{x-\sqrt{3}}=3x+\sqrt{3}\)

\(\Leftrightarrow\sqrt{x}.\sqrt{x-\sqrt{3}}=0\Rightarrow\orbr{\begin{cases}x=0\\x=\sqrt{3}\end{cases}}\)

Vì x = 0 không thỏa ĐKXĐ vậy PT nhận nghiệm duy nhất là \(x=\sqrt{3}\)

x= 0.761322463768116,

x= 0.369494467346496,

x=1.57660410301179

\(A=\sqrt{4x+1}-\sqrt{3x-2}=\frac{x+3}{2}\)

đkxđ \(\hept{\begin{cases}x\ge-\frac{1}{4}\\x\ge\frac{2}{3}\end{cases}}\)

đặt t=x+3 phương trình trở thành 

\(A=\sqrt{4\left[x+3\right]-11}-\sqrt{3\left[x+3\right]-11}=\frac{x+3}{2}\)

\(A=\sqrt{4t-11}-\sqrt{3t-11}=\frac{t}{2}\)

\(\Leftrightarrow4t-11=\frac{t^2}{4}+3t-11+t\sqrt{3t-11}\)

\(\Leftrightarrow t^2-\frac{t^2}{4}=t\sqrt{3t-11}\)

\(\Leftrightarrow\frac{t\left[4-t\right]}{4}=t\sqrt{3t-11}\)

\(\Leftrightarrow\frac{\left[4-t\right]^2}{16}=3t-11\)

\(\Leftrightarrow t^2-56t+192=0\)

\(\Leftrightarrow\orbr{\begin{cases}t=28+4\sqrt{37}\\t=28-4\sqrt{37}\end{cases}}\)

thế vào x+3=t suy ra 

\(\orbr{\begin{cases}x=25+4\sqrt{37}\left[loại\right]\\x=25-4\sqrt{37}\left[nhận\right]\end{cases}}\)

\(S=\left\{25-4\sqrt{37}\right\}\)

nhiều thế giải ko đổi đâu bạn

vậy trả lời câu a thôi

đkxđ : \(\frac{1}{2}\le x\le7\)

\(x^2-5x+3\sqrt{2x-1}=2\sqrt{14-2x}+5\)

\(\Leftrightarrow\left(x^2-5x\right)+3\left(\sqrt{2x-1}-3\right)=2\left(\sqrt{14-2x}-2\right)\)

\(\Leftrightarrow x\left(x-5\right)+\frac{3.\left(2x-10\right)}{\sqrt{2x-1}+3}+\frac{2.\left(2x-10\right)}{\sqrt{14-2x}+2}=0\)

\(\Leftrightarrow\left(x-5\right)\left(x+\frac{6}{\sqrt{2x-1}+3}+\frac{4}{\sqrt{14-2x}+2}\right)=0\)

\(\Leftrightarrow x=5\)

còn bài a,c lười đánh lắm