Question

Решить неравенство! (3^(x+1)+3^(2-x))*x> =28*x

Answer 1

$(3^{x+1}+3^{2-x}-28)*x \geq 0\\ 3^x=a,a\ \textgreater \ 0\\ 3a+ \frac{9}{a} -28=0\\ 3a^2-28a+9=0\\ D=784-108=676=26^2\\ a_1= \frac{28-26}{6} = \frac{1}{3} =\ \textgreater \ x=-1\\ a_2= \frac{28+26}{6} =9=\ \textgreater \ x=2\\ ....-........[-1]......+.........[0]...........-...........[2]........+........$

ответ: x∈[-1;0]U[2;+∞)