A=\(x^2+y^2+9+2xy+6x+6y+9-x^2-y^2-9\)

A=2xy+6x+6y

B=\(25x^2-4-25x^2+10x-1\)

B=10x-5

C=\(100^2+98^2+...+2^2-\left(99^2+97^2+...+1\right)\)

C=\(100^2-99^2+98^2-97^2+...+4^2-3^2+2^2-1\)

C=\(\left(100-99\right)\left(100+99\right)+...+\left(2-1\right)\left(2+1\right)\)

C=\(199+195+191+...+7+3\)

C=\(\left(199+3\right)\left(\left(199-3\right):4+1\right)=10100\)

\(\dfrac{x}{3}=\dfrac{y}{4}=\dfrac{z}{5}=\dfrac{x.y.z}{3.4.5}=\dfrac{60}{60}=1\)

với \(\dfrac{x}{3}=1\Rightarrow x=3\)

\(\dfrac{y}{4}=1\Rightarrow y=4\)

\(\dfrac{z}{5}=1\Rightarrow z=5\)

A<\(\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{2011.2012}+\dfrac{1}{2012.2013}\)

A<\(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{2011}-\dfrac{1}{2012}+\dfrac{1}{2012}-\dfrac{1}{2013}\)

A<\(\dfrac{1}{2}-\dfrac{1}{2013}\)

A<\(\dfrac{2011}{4026}< 1\)

Vì A bé hơn 1 nên A không phải là số tự nhiên