Question

Решите уравнение
2^2-x-2^x-1=1

Answer 1

$\displaystyle 2^{2-x}-2^{x-1}=1\\\\\frac{2^2}{2^x}-\frac{2^x}{2}=1\\\\2^x=t; t>0\\\\\frac{4}{t}-\frac{t}{2}=1\\\\\frac{8-t^2}{2t}=1\\\\8-t^2=2t\\\\t^2+2t-8=0\\\\D=4+32=36\\\\t_{1.2}=\frac{-2 \pm 6}{2}\\\\t_1=-4; t_2=2\\\\2^x=2; x=1\\\\2^x\neq -4$

Ответ х=1