2 x + 1 + 2 − x + 1 = 5 {\displaystyle 2^{x+1}+2^{-x+1}=5}
2 x + 1 + 2 − x + 1 = 5 2 x ∗ 2 + 2 2 x = 5 2 2 x + 2 = 5 ∗ 2 x 2 x = t 2 t 2 + 2 − 5 t = 0 ( t − 2 ) ( t − 1 2 ) = 0 t = 2 t = 1 2 2 x = 2 2 x = 2 − 1 x = 1 x = − 1 {\displaystyle {\begin{aligned}2^{x+1}+2^{-x+1}=5\\2^{x}*2+{\frac {2}{2^{x}}}=5\\2^{2x}+2=5*2^{x}\\2^{x}=t\\2t^{2}+2-5t=0(t-2)(t-{\frac {1}{2}})=0\\t=2\ \ \ \ \ t={\frac {1}{2}}\\2^{x}=2\ \ \ \ \ \ 2^{x}=2^{-1}\\x=1\ \ \ \ \ \ x=-1\\\end{aligned}}}
