Question

Dacă $a^2=2014^4-2 \times2013^2 -4 \times 2014 + 3$ , calculați a.

Answer 1

Am atasat rezolvarea!

Answer 2

$a^2= 2014^2-2\times2013^2-4\times2014+3 \\ \\ a^2 = 2014^2-2\times(2014-1)^2-4\times2014+3 \\ \\ a^2 = 2014^4-2\times(2014^2-2\times 2014 +1) -4\times2014+3 \\ \\ a^2 = 2014^4 -2\times 2014^2 +4\times 2014 -4\times 2014-2+3 \\ \\ a^2 = 2014^4 -2\times2014^2 +1 \\ \\ a^2 = (2014^2-1)^2 \\ \\ \boxed{ a = \pm (2014^2-1)}$