Ta có:
($\sqrt{2012}$+$\sqrt{2014}$)²=($\sqrt{2012}$)²+2.$\sqrt{2012}$.$\sqrt{2014}$($\sqrt{2014}$)²
⇔2012+2.$\sqrt{2012}$.$\sqrt{2014}$+2014
⇔4026+2.$\sqrt{(2013-1)(2013+1)}$
⇔4026+2$\sqrt{2013²-1²}$<4026+2$\sqrt{2013}$
⇔2.2013+2.2013
⇔4.2013
⇔(2$\sqrt{2013}$)²
⇒($\sqrt{2012}$+$\sqrt{2014}$)²<(2$\sqrt{2013}$)²
⇒$\sqrt{2012}$+$\sqrt{2014}$<2$\sqrt{2013}$
Vậy $\sqrt{2012}$+$\sqrt{2014}$<2$\sqrt{2013}$
#NOCOPY
#NOPLAGIARISM