b) \(xy+3x-2y=11\)

\(xy+3x-2y-6=11-6\)

\(xy+3x-2y-6=5\)

\(\left(xy+3x\right)-\left(2y+6\right)=5\)

\(x\left(y+3\right)-2\left(y+3\right)=5\)

\(\left(x-2\right)\left(y+3\right)=5\)

\(\Rightarrow5=\left(-1\right)\left(-5\right)=1\cdot5\)

Bạn tự lập bảng mà thử nghiệm nhé

Ngu vcl

a) \(xy+3x-7y=21\)

\(xy+3x-7y-21=21-21\)

\(xy+3x-7y-21=0\)

\(\left(xy+3x\right)-\left(7y+21\right)=0\)

\(x\left(y+3\right)-7\left(y+3\right)=0\)

\(\left(x-7\right)\left(y+3\right)=0\)

\(\orbr{\begin{cases}x-7=0\\y+3=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=7\\y=-3\end{cases}}\)

a: \(\left(x,y\right)\in\left\{\left(-9;1\right);\left(-1;9\right);\left(-3;3\right)\right\}\)

b: \(\left(x,y\right)\in\left\{\left(1;7\right);\left(-7;-1\right)\right\}\)

c: \(\left(x,y\right)\in\left\{\left(11;-1\right);\left(-11;1\right)\right\}\)

a: 

b: 

c: 

a: \(\left(x,y\right)\in\left\{\left(-9;1\right);\left(-1;9\right);\left(-3;3\right)\right\}\)

b: \(\left(x,y\right)\in\left\{\left(1;7\right);\left(-7;-1\right)\right\}\)

c: \(\left(x,y\right)\in\left\{\left(11;-1\right);\left(-1;11\right)\right\}\)

Ta có: \(xy\le\dfrac{\left(x+y\right)^2}{4}=\dfrac{121}{4}\)

Tổng không đổi, tích lớn nhất khi x = y = 5,5

xy\(_{max}\) = 5,5\(^2\) =\(\frac{121}{4}\)

\(\text{a) Ta có:}xy=1\Rightarrow\hept{\begin{cases}2xy=2\\-2xy=-2\end{cases}}\)

\(\text{Ta lại có: }x^2+y^2=2\Rightarrow\hept{\begin{cases}x^2+y^2+2xy=2+2=4\\x^2+y^2-2xy=2-2=0\end{cases}\Rightarrow\hept{\begin{cases}\left(x+y\right)^2=4\\\left(x-y\right)^2=0\end{cases}\Rightarrow}\hept{\begin{cases}x+y=\pm2\\x-y=0\end{cases}}}\)

\(\text{b) Ta có: }x+y=5\)

\(\Rightarrow\left(x+y\right)^2=25\)

\(\Rightarrow x^2+2xy+y^2=25\)

\(\Rightarrow x^2+4+y^2=25\)

\(\Rightarrow x^2+y^2=21\)

\(\text{b) Ta có: }x^2+y^2=21\)

\(\Rightarrow x^2-2xy+y^2=21-2xy\)

\(\Rightarrow\left(x-y\right)^2=21-4\)

\(\Rightarrow\left(x-y\right)^2=17\)

\(\Rightarrow x-y=\pm\sqrt{17}\)

Theo bài ra ta có:

\(x^2y+xy^2+x+y=2010\)

\(\Rightarrow xy\left(x+y\right)+\left(x+y\right)=2010\)

\(\Rightarrow\left(x+y\right)\left(xy+1\right)=2010\)

\(\Rightarrow\left(x+y\right)\left(11+1\right)=2010\)

\(\Rightarrow12\left(x+y\right)=2010\Rightarrow x+y=2010\div12=167,5\)

Ta có: \(A=x^4+y^4=\left(x^2\right)^2+2x^2y^2+\left(y^2\right)^2-2x^2y^2\)

\(=\left(x^2+y^2\right)^2-2\left(xy\right)^2\)

\(=\left[\left(x+y\right)^2-2xy\right]^2-2\times11^2\)

\(\Rightarrow\left[\left(167,5\right)^2-2.11\right]^2-245\)

\(\Rightarrow\left(28056,25-22\right)^2-245=785918928,0625\)

x+y+x.y=11 suy ra x+x.y+y=11 suy ra x.(x+y)+y=11

rồi típ theo tự làm nha

x=2;y=3

x=3;y=2