Нужно решение [latex]5*25^{1/x} + 3*10^{1/x} \geq 2*4^{1/x}[/latex]

[latex]5*25^{\frac{1}{x}}+3*10^{\frac{1}{x}} \geq 2*4^{\frac{1}{x}};\\\\x \neq 0;\\\\5*(\frac{25}{4})^{\frac{1}{x}}+3*(\frac{10}{4})^{\frac{1}{x}}-2 \geq 0;\\\\5*((\frac{5}{2})^{\frac{1}{x}})^2+3*(\frac{5}{2})^{\frac{1}{x}}-2 \geq 0;\\\\[/latex] [latex]\frac{5}{2}^{\frac{1}{x}}=t>0;\\\\5t^2+3t-2 \geq 0;\\\\ (5t-2)(t+1) \geq 0;\\\\t \leq -1;V;t \geq \frac{2}{5};\\\\t \geq \frac{2}{5};\\\\ (\frac{5}{2})^{\frac{1}{x}} \geq \frac{2}{5};\\\\(\frac{5}{2})^{\frac{1}{x}} \geq (\frac{5}{2})^{-1};\\\\ \frac{5}{2} \geq 1;\\\\\frac{1}{x} \geq -1;\\\\\frac{1+x}{x} \geq 0;\\\\x \leq -1;V;x>0;\\\\ (-\infty; -1] \cup (0;+\infty)[/latex]