[tex]x^2=2009 \cdot 2010\cdot 2011 \cdot 2012 + 1\\
x^2=2009\cdot (2009+3) \cdot (2009+1)\cdot (2009+2)+1\\
x^2=(2009^2+3\cdot 2009)\cdot (2009^2+2\cdot 2009+2009+2)+1\\
x^2=(2009^2+3\cdot 2009)\cdot (2009^2+3\cdot 2009 +2)+1\\
Notam: a=2009^2+3\cdot 2009\\
x^2=a(a+2)+1\\
x^2=a^2+2a+1\\
x^2=(a+1)^2\\
Asadar:\\
x^2=(2009^2+3\cdot 2009 +1)^2\\
Deci: x=2009^2+3\cdot 2009 + 1\\
\text{Poti sa calculezi singur.}[/tex]
