Bài 1:
\(A=\frac{356^2-144^2}{256^2-244^2}\)
\(=\frac{\left(356-144\right)\left(356+144\right)}{\left(256-244\right)\left(256+244\right)}=\frac{212\cdot500}{12\cdot500}\)
\(=\frac{212}{12}=\frac{53}{3}\)
\(B=253^2+94\cdot253+47^2\)
\(=253^2+2\cdot253\cdot47+47^2\)
\(=\left(253+47\right)^2=300^2=90000\)
\(C=163^2-2\cdot163\cdot46+46^2\)
\(=\left(163-46\right)^2\)
\(=117^2=13689\)
\(D=\left(100^2+98^2+\cdots+2^2\right)-\left(99^2+97^2+\cdots+1^2\right)\)
\(=\left(100^2-99^2\right)+\left(98^2-97^2\right)+\ldots+\left(2^2-1^2\right)\)
=(100-99)(100+99)+(98-97)(98+97)+...+(2-1)(2+1)
=100+99+98+97+...+2+1
\(=100\cdot\frac{101}{2}=101\cdot50=5050\)
Bài 2:
a; \(A=5x^2+5y^2+8xy+2y-2x+2020\)
\(=x^2-2x+1+y^2+2y+1+4x^2+8xy+4y^2+2018\)
\(=\left(x-1\right)^2+\left(y+1\right)^2+4\left(x+y\right)^2+2018\ge2018\forall x,y\)
Dấu '=' xảy ra khi \(\begin{cases}x-1=0\\ y+1=0\\ x+y=0\end{cases}\Rightarrow\begin{cases}x=1\\ y=-1\\ x=-y\end{cases}\)
=>x=1 và y=-1
