a)
\(VP=\left(x+y\right)^2=\left(x+y\right)\left(x+y\right)=x\left(x+y\right)+y\left(x+y\right)=\)
\(=x^2+xy+xy+y^2=x^2+xy\left(1+1\right)+y^2=x^2+2xy+y^2=VT\)
b)
\(A=!x+y!^2=x^2+2xy+y^2\\\)
\(B=\left(!x!+!y!\right)^2=x^2+2!x!.!y!+y^2\\ \)
\(B-A=2!xy!-2xy=2\left(!xy!-xy\right)\) \(\Leftrightarrow\left[\begin{matrix}\left\{\begin{matrix}xy\ge0\\2.\left(xy-xy\right)=0\end{matrix}\right.\\\left\{\begin{matrix}xy< 0\\2\left(-xy-xy\right)=-4xy>0\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[\begin{matrix}\left\{\begin{matrix}xy\ge0\\B-A=0\end{matrix}\right.\\\left\{\begin{matrix}xy< 0\\B-A>0\end{matrix}\right.\end{matrix}\right.\\\) \(\Leftrightarrow\left[\begin{matrix}\left\{\begin{matrix}xy\ge0\\B=A\end{matrix}\right.\\\left\{\begin{matrix}xy< 0\\B>A\end{matrix}\right.\end{matrix}\right.\) \(\Rightarrow B\ge A\)
đẳng thức khi xy>=0 => dpcm
c)
\(A=!x-2017!+!x-1!=!x-2017!+!1-x!\ge!\left(x-2017\right)+\left(1-x\right)!=!-2016!=2016\)
Đẳng thức khi (x-2017)(1-x)>=0=> 1<=x<=2017
