Question

Решите неравенствоооооо

Answer 1

$3^{log_3(x)}+x^{log_3(x)}\ \textgreater \ 2 \sqrt[4]{3} \\ODZ:\\x\ \textgreater \ 0 \\log_3(x)=t\\x=3^t\\3^{t^2}+3^{t^2}\ \textgreater \ 2 \sqrt[4]{3} \\3^{t^2}=y\\2y\ \textgreater \ 2 \sqrt[4]{3} \\y\ \textgreater \ \sqrt[4]{3} \\3^{t^2}\ \textgreater \ \sqrt[4]{3} \\t^2\ \textgreater \ \frac{1}{4}\\|t|\ \textgreater \ \frac{1}{2} \\t\ \textgreater \ \frac{1}{2} \\t\ \textless \ -\frac{1}{2}$
t∈(-∞;1/2)∪(1/2;+∞)
$\left \{ {{t\ \textless \ -\frac{1}{2} } \atop {t\ \textgreater \ \frac{1}{2} }} \right. \left \{ {{log_3(x)\ \textless \ -\frac{1}{2} } \atop {log_3(x)\ \textgreater \ \frac{1}{2} }} \right.$
$\left \{ {{x\ \textless \ \frac{ \sqrt{3} }{3} } \atop {x\ \textgreater \ \sqrt{3} }} \right.$
x∈(0;$\frac{ \sqrt{3} }{3}$)∪($\sqrt{3}$;+∞)