Question

нужно решение

$5*25^{1/x} + 3*10^{1/x} geq 2*4^{1/x}$

Answer 1

$frac{5}{2}^{frac{1}{x}}=t>0;\\5t^2+3t-2 geq 0;\\ (5t-2)(t+1) geq 0;\\t leq -1;V;t geq frac{2}{5};\\t geq frac{2}{5};\\ (frac{5}{2})^{frac{1}{x}} geq frac{2}{5};\\(frac{5}{2})^{frac{1}{x}} geq (frac{5}{2})^{-1};\\ frac{5}{2} geq 1;\\frac{1}{x} geq -1;\\frac{1+x}{x} geq 0;\\x leq -1;V;x>0;\\ (-infty; -1] cup (0;+infty)$

$5*25^{frac{1}{x}}+3*10^{frac{1}{x}} geq 2*4^{frac{1}{x}};\\x neq 0;\\5*(frac{25}{4})^{frac{1}{x}}+3*(frac{10}{4})^{frac{1}{x}}-2 geq 0;\\5*((frac{5}{2})^{frac{1}{x}})^2+3*(frac{5}{2})^{frac{1}{x}}-2 geq 0;$

[tex]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)" />