Răspuns:
[tex] {25}^{x} o {5}^{x} = {25}^{x} + {5}^{x} + 2016 \\ {25}^{x} + {5}^{x} + 2016 = 2046 \\ {( {(5)}^{2} )}^{x} + {5}^{x} = 2046 - 2016 \\ {( {(5}^{x} )}^{2} + {5}^{x} = 20[/tex]
notam
[tex] {5}^{x} = t = > {t}^{2} + t - 20 = 0[/tex]
[tex]delta \: = {b}^{2} - 4ac[/tex]
nu am avut semn pt delta
[tex]1 + 80 = 81[/tex]
[tex]x1 = \frac{ - b + \sqrt{81} }{2a} = \frac{ - 1 + 9}{2} = 4[/tex]
[tex]x2 = \frac{ - 1 - 9}{2} = - 5[/tex]
renotam:
[tex] {5}^{x} = 4 \: \\nu \: avem \: sol.[/tex]
[tex] {5}^{x} = - 5nu \: are \: sol.[/tex]
[tex] \sqrt{x - 2} + \sqrt{2 - x} + 2016 = 2016 \\ \sqrt{x - 2} + \sqrt{2 - x} = 0 \\ \sqrt{x - 2} = - \sqrt{2 - x} \: ridicam \: la \: patrat \\ \\ x - 2 = 2 - x = > x - 2 - 2 + x = 0 \\ 2x - 4 = 0 \\ 2x = 4 = > x = 2[/tex]
