Question

решить неравенство $(0,25)^{x^{2} - 4} -16 * ( frac{1}{4} )^{x} > 0$

Answer 1

$(0,25)^{x^2-4}-16cdot (frac{1}{4})^{x} textgreater 0\\0,25= frac{1}{4}=4^{-1}; ,; ; 16=4^2\\(4^{-1})^{x^2-4}-4^2cdot 4^{-x} textgreater 0\\4^{-x^2+4}-4^{2-x} textgreater 0\\4^{-x^2+4} textgreater 4^{2-x}\\-x^2+4 textgreater 2-x\\x^2-x-2 textless 0; ,; ; ; x_1=-1,; ; x_2=2; (teorema; Vieta)\\(x+1)(x-2) textless 0\\+++(-1)---(2)+++\\xin (-1,2)$