Ta có : 

\(P=8x^2+3y^2-8xy-6y+21\)

\(=\left(8x^2-8xy+2y^2\right)+\left(y^2-6y+9\right)+12\)

\(=2\left(4x^2-4xy+y^2\right)+\left(y-3\right)^2+12\)

\(=2\left(2x-y\right)^2+\left(y-3\right)^2+12\)

Ta có 

\(2\left(2x-y\right)^2+\left(y-3\right)^2\ge0\) với mọi x , y 

Suy ra : 

\(2\left(2x-y\right)^2+\left(y-3\right)^2+12\ge12\)

\(\Leftrightarrow P\ge12\)

 Dấu " = " xảy ra khi \(2x-y=y-3=0\) .  Suy ra  \(x=\frac{3}{2},y=3\)

Vậy GTNN của P là 12, đạt được khi \(x=\frac{3}{2},y=3\)

Câu a ) 

\(ĐKXĐx\ne-1,3\)

Ta có : 

\(\frac{x}{2x+2}-\frac{2x}{x^2-2x-3}=\frac{x}{6-2x}\)

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

\(\Rightarrow\frac{x}{2\left(x+1\right)}.2\left(x+1\right)\left(x-3\right)-\frac{2x}{\left(x+1\right)\left(x-3\right)}.2\left(x+1\right)\left(x-3\right)\)

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

=> x(x-3) -4x =−x(x+1)

=> \(x^2-7x=-x^2-x\)

\(\Rightarrow2x^2-6x=0\)

\(\Rightarrow2x\left(x-3\right)=0\)

\(\Rightarrow x\in\left\{3,0\right\}\)

Câu b ) 

Ta có : 

\(\hept{\begin{cases}\sqrt{2}x-3y=2006\\2x+\sqrt{3}y=2007\end{cases}}\)

\(\Rightarrow\hept{\begin{cases}\sqrt{2}x-3y=2006\\2\sqrt{3}x+3y=2007\sqrt{3}\end{cases}}\)

\(\Rightarrow\hept{\begin{cases}\sqrt{2}x-3y=2006\\2\sqrt{3}x+3y+\sqrt{2}x-3y=2007\sqrt{3}+2006\end{cases}}\)

\(\Rightarrow\hept{\begin{cases}\sqrt{2}x-3y=2006\\\left(\sqrt{2}+2\sqrt{3}\right)x=2007\sqrt{3}+2006\end{cases}}\)

\(\Rightarrow\hept{\begin{cases}y=\frac{\sqrt{2}x-2006}{3}\\x=\frac{2007\sqrt{3}+2006}{\sqrt{2}+2\sqrt{3}}\end{cases}}\)

\(\hept{\begin{cases}y=\frac{\sqrt{2}.\frac{2007\sqrt{3}+2006}{\sqrt{2}+2\sqrt{3}}-2006}{3}\\x=\frac{2007\sqrt{3}+2006}{\sqrt{2}+2\sqrt{3}}\end{cases}}\)

\(\Rightarrow\hept{\begin{cases}y=\frac{2007\sqrt{6}-4012\sqrt{3}}{\left(\sqrt{2}+2\sqrt{3}\right).3}\\x=\frac{2007\sqrt{3}+2006}{\sqrt{2}+2\sqrt{3}}\end{cases}}\)

chieu dai mah vuon la a , rog la a -40

S vuon = S be boi + S loi di

a (a -40)= 6000 + 2 ( a.10+ (a -60).100)

=> Dai manh vuon :a =120 ,rog =80

Nham (a -40) a= 6000 + 2 ( a.10 + (a-60).10)

\(\hept{\begin{cases}mx-y=2m\left(1\right)\\4x-my=m+6\left(2\right)\end{cases}}\)

Từ (1) ta có: y=mx-2m, thay y vào (2) ta được

\(4x-m\left(mx-2m\right)=m+6\)

\(\Leftrightarrow\left(4-m^2\right)x=-2m^2+m+6\)

\(\Leftrightarrow\left(m^2-4\right)x=\left(2m+3\right)\left(m-2\right)\left(3\right)\)

Nếu \(m^2-4\ne\)0 hay m\(\ne\pm\)2 thì \(x=\frac{2m+3}{m+2}\)

Khi đó: \(y=mx-2m=\frac{2m^2+3m}{m+2}-2m=-\frac{m}{m+2}\)

Hệ có nghiệm duy nhất \(\left(\frac{2m+3}{m+2};\frac{-m}{m+2}\right)\)

Nếu m=2 thì (3) thỏa mãn với mọi x, và khi đó y=mx-2m=2x-4

Hệ vô số nghiệm \(\left(x;2x-4\right)\)với \(x\inℝ\)

Nếu m=-2 thì (3) trở thành 0x=4. Hệ vô nghiệm

\(x\left(3+x\right)\left(x^2+6\right)=4\left(x^2-4x+4\right)\)

\(3x^3+18x+x^4+6x^2=4x^2-16x+16\)

\(3x^3+18x+x^4+6x^2-4x^2+16x-16=0\)

\(3x^2+34x+x^4+2x^2-16=0\)

=> vô nghiệm