Question

x×x=2009×2010×2011×2012+1
trebuie aflat x

Answer 1

[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]