a) Đặt \(a=\frac{1}{\sqrt{x-4}},b=\frac{1}{y+2}\) từ đây ta có

\(\Rightarrow\left\{{}\begin{matrix}3a+4b=7\\5a-1b=4\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}3a+4b=7\\20a-4b=16\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}23a=23\\3a+4b=7\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}a=1\\b=1\end{matrix}\right.\).

\(\Rightarrow\left\{{}\begin{matrix}\frac{1}{\sqrt{x-4}}=1\\\frac{1}{y+2}=1\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}x-4=1\\y+2=1\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=5\\y=-1\end{matrix}\right.\)

b) Theo đề bài ta có hệ pt

\(\left\{{}\begin{matrix}u^2+v^2=65\\uv=-28\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}\left(u+v\right)^2-uv=65\\uv=-28\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}\left(x+y\right)^2=65+2.\left(-28\right)=9\\uv=-28\end{matrix}\right.\)

TH1 : \(\left\{{}\begin{matrix}u+v=3\\uv=-28\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}u=3-v\\\left(3-v\right)v=-28\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}v=-4\Rightarrow u=7\\v=7\Rightarrow u=-4\end{matrix}\right.\)

TH2 \(\left\{{}\begin{matrix}u+v=-3\\uv=-28\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}u=-3-v\\\left(-3-v\right)v=-28\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}v=-7\Rightarrow u=4\\v=4\Rightarrow u=-7\end{matrix}\right.\)

Vậy .......

a) \(\hept{\begin{cases}3\left(x+1\right)+2\left(x+2y\right)=4\\4\left(x+1\right)-\left(x+2y\right)=9\end{cases}}\Leftrightarrow\hept{\begin{cases}3\left(x+1\right)+2\left(x+2y\right)=4\\8\left(x+1\right)-2\left(x+2y\right)=18\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}11\left(x+1\right)=22\\3\left(x+1\right)+2\left(x+2y\right)=4\end{cases}}\Leftrightarrow\hept{\begin{cases}x=1\\4y+8=4\end{cases}}\Leftrightarrow\hept{\begin{cases}x=1\\y=-1\end{cases}}\)

b) ĐK : y khác 0

\(\hept{\begin{cases}x+\frac{1}{y}=-\frac{1}{2}\\2x-\frac{3}{y}=-\frac{7}{2}\end{cases}}\Leftrightarrow\hept{\begin{cases}3x+\frac{3}{y}=-\frac{3}{2}\\2x-\frac{3}{y}=-\frac{7}{2}\end{cases}}\Leftrightarrow\hept{\begin{cases}5x=-5\\3x+\frac{3}{y}=-\frac{3}{2}\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}x=-1\\-3+\frac{3}{y}=-\frac{3}{2}\end{cases}}\Leftrightarrow\hept{\begin{cases}x=-1\\\frac{3}{y}=\frac{3}{2}\end{cases}}\Leftrightarrow\hept{\begin{cases}x=-1\\y=2\left(tm\right)\end{cases}}\)

cho mk hỏi ai chs lazi điểm danh cái đê ~ mk hỏi thật đấy k đùa nha ~ bình luận thì mk k cho 3 cái ~

\(C,\hept{\begin{cases}\left|x-1\right|+\left|y-2\right|=1\\\left|x-1\right|+3y=3\left(#\right)\end{cases}}\)

\(\Rightarrow3y-\left|y-2\right|=2\)(1)

*Nếu y > 2 thì 

\(\left(1\right)\Leftrightarrow3y-y+2=2\)

        \(\Leftrightarrow y=0\)(Loại do ko tm KĐX)

*Nếu y < 2 thì

\(\left(1\right)\Leftrightarrow3y-2+y=2\)

\(\Leftrightarrow y=1\)(Tm KĐX)

Thay y = 1 vào (#) được \(\left|x-1\right|+3=3\)

                                    \(\Leftrightarrow x=1\)

Vậy hệ có nghiệm \(\hept{\begin{cases}x=1\\y=1\end{cases}}\)

\(A,ĐKXĐ:x\left(y+1\right)>0\)

\(\hept{\begin{cases}x+y=5\left(1\right)\\\sqrt{\frac{x}{y+1}}+\sqrt{\frac{y+1}{x}}=2\left(2\right)\end{cases}}\)

Giải (2) 

Có bđt \(\frac{a}{b}+\frac{b}{a}\ge2\left(a,b>0\right)\)

Nên \(\sqrt{\frac{x}{y+1}}+\sqrt{\frac{y+1}{x}}\ge2\)

Dấu "=" xảy ra \(\Leftrightarrow x=y+1\)

Thế x = y + 1 vảo pt (1) được

\(y+1+y=5\)

\(\Leftrightarrow y=2\)

\(\Rightarrow x=2+1=3\)

Thấy x = 3 ; y = 2 thỏa mãn ĐKXĐ
Vậy hệ có ngihiemej \(\hept{\begin{cases}x=3\\y=2\end{cases}}\)

c) Ta có: \(\left\{{}\begin{matrix}\dfrac{x+2}{x+1}+\dfrac{2}{y-2}=6\\\dfrac{5}{x+1}-\dfrac{1}{y-2}=3\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{1}{x+1}+\dfrac{2}{y-2}=5\\\dfrac{5}{x+1}-\dfrac{1}{y-2}=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{5}{x+1}+\dfrac{10}{y-2}=25\\\dfrac{5}{x+1}-\dfrac{1}{y-2}=3\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{11}{y-2}=22\\\dfrac{1}{x+1}+\dfrac{2}{y-2}=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y-2=\dfrac{1}{2}\\\dfrac{1}{x+1}=1\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x+1=1\\y-2=\dfrac{1}{2}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=0\\y=\dfrac{5}{2}\end{matrix}\right.\)