Question

[Tấn Lộc Đào]

4 mũ n+2  +   4 mũ n+3  +  4 mũ n+4  +  4 mũ n+5 = 85 x (2 mũ 2019 : 2 mũ 2015)

Answer 1

[Đoàn Đức Hà]

\(4^{n+2}+4^{n+3}+4^{n+4}+4^{n+5}=85.\left(2^{2019}\div2^{2015}\right)\)

\(\Leftrightarrow4^{n+2}\left(1+4^1+4^2+4^3\right)=85.2^{2019-2015}\)

\(\Leftrightarrow4^{n+2}.85=85.2^4\)

\(\Leftrightarrow4^{n+2}=2^4=4^2\)

\(\Leftrightarrow n+2=2\)

\(\Leftrightarrow n=0\)