Question

5^x+1 + 5^x + 5^x-1=775

Answer 1

EAE VELHO,

use a propriedade da exponenciação..

$\boxed{a^{m+n}\Rightarrow a^m\cdot a^n}\\\\ \boxed{a^{-1}\Rightarrow\dfrac{1}{a^1}\Rightarrow\dfrac{1}{a}}\\\\ 5^{x+1}+5^x+5^{x-1}=775\\ 5^x\cdot5^1+5^x+5^x\cdot5^{-1}=775\\\\ poe~5^x~em~evidencia..\\\\ 5^x\cdot(1+5^1+5^{-1})=775\\ 5^x\cdot\left(1+5+ \dfrac{1}{5}\right)=775\\\\ 5^x\cdot\left( \dfrac{31}{5}\right)=775\\\\ 5^x=775\div \dfrac{31}{5}\\\\ 5^x=125\\ \not5^x=\not5^3\\ x=3\\\\\\ \huge\boxed{\boxed{S=\{3\}}}$

Tenha ótimos estudos ;D