22-21-3213-3124-4-24-2-4-143

\(\left(4x+1\right)\left(x-2\right)-\left(2x-3\right)\left(2x+1\right)=7\)

\(\Leftrightarrow4x^2-8x+x-2-\left(4x^2+2x-6x-3\right)=7\)

\(\Leftrightarrow4x^2-7x-2-4x^2+4x+3=7\)

\(\Leftrightarrow-3x+1=7\)

\(\Leftrightarrow-3x=6\Leftrightarrow x=-2\)

\(\left(x-1\right)\left(x+2\right)-x-2=0\)

\(\Leftrightarrow\left(x+2\right)\left(x-1-1\right)=0\)

\(\Leftrightarrow\left(x+2\right)\left(x-2\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x=-2\\x=2\end{cases}}\)

a)\(\left(x+y\right)^2+\left(x-y\right)^2-2\left(x-y\right)\left(x+y\right)\)

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

b) \(9x^2-49=0\)

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

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

c) \(\left(x+3\right)\left(x^2-3x+9\right)-x\left(x-1\right)\left(x+1\right)-27=0\)

\(\Leftrightarrow x^3+27-x\left(x^2-1\right)-27=0\)

\(\Leftrightarrow x^3+27-x^3+x-27=0\)

\(\Leftrightarrow x=0\)

\(\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}+\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}\)

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

\(=\frac{3-2\sqrt{3}.\sqrt{2}+3+2\sqrt{3}.\sqrt{2}+2}{3-2}\)

\(=3+2+3+2=10\)

\(A=x^2+y^2-xy-3y+2016\)

\(\Leftrightarrow A=\left(x^2-xy+\frac{y^2}{4}\right)+\left(\frac{3y^2}{4}-3y+3\right)+2013\)

\(\Leftrightarrow A=\left(x-\frac{y}{2}\right)^2+3\left(\frac{y}{2}-1\right)^2+2013\ge2013\)

Dấu '' = '' xảy ra khi và chỉ khi \(\hept{\begin{cases}x-\frac{y}{2}=0\\\frac{y}{2}-1=0\end{cases}\Leftrightarrow\hept{\begin{cases}x=\frac{y}{2}\\\frac{y}{2}=1\end{cases}\Leftrightarrow}\hept{\begin{cases}x=1\\y=2\end{cases}}}\)

Vậy Min A= 2013 \(\Leftrightarrow\hept{\begin{cases}x=1\\y=2\end{cases}}\)

A=(x^2-xy+1/4 . y^2)+3(1/4. y^2 -y +1)+2013

=(x-1/2y)^2 +3(1/2y-1)^2+2013 

Mà (x-1/2y)^2>=0 ; (1/2y-1)^2>=0

=> A>=2013

Dấu = xảy ra <=> x=1/2y và 1/2y=1 <=> x=1 và y=2