Question

Помогите решить неравенство 6.50 (а), пожалуйста

Answer 1

$3^{x+4}+3^{-x-3} textgreater 4\ 3^x=m, m textgreater 0\ 3^4*m +frac{1}{3^3*m} textgreater 4\ 81m+ frac{1}{27m} textgreater 4/*27m\ 2187m^2+1-108m textgreater 0\ 2187m^2-108m+1 textgreater 0\ D=(-108)^2-4*2187=54^2\ m_1= frac{108-54}{2*2187} = frac{1}{81} \ m_2= frac{108+54}{2*2187} = frac{1}{27} \ (m- frac{1}{81} )(m- frac{1}{27} ) textgreater 0\ -infty textless m textless frac{1}{27} , frac{1}{81} textless m textless +infty\ 3^x textless 3^{-3}, 3^x textgreater 3^{-4}\ x textless -3, x textgreater -4\ xin(-infty;-4)U(-3;+infty)$