js","1717","static/chunks/1717-e9687bfca52045a6.js","8117","static/chunks/8117-3a5cb76430604345.js","1464","static/chunks/1464-4de8faf93b802138.js","422","static/chunks/422-b1f5ec985dcfd2ef.js","3169","static/chunks/3169-0b225cc6264f1f70.js","5791","static/chunks/5791-b7519a5ea5ac96a7.js","4839","static/chunks/4839-abf7392d0b162b93.js","5322","static/chunks/5322-2dee03e10531d285.js","1493","static/chunks/1493-0e365f06d2d7ff74.js","3910","static/chunks/3910-d35f7a55e63a44d2.js","2661","static/chunks/2661-5a8e341dbac91d3f.js","6986","static/chunks/app/(unauthorized-user)/testing/%5BexamType%5D/%5B...slug%5D/page-3d61388e5ed47f00.js"],""] 46:T633, $\frac{5^x}{5^x-4}+\frac{5^x+5}{5^x-5}+\frac{22}{25^x-9\cdot 5^x+20}\le 0.$

$\text{Пусть } 5^x=t. \text{ Тогда неравенство примет вид:}$

$\frac{t}{t-4}+\frac{t+5}{t-5}+\frac{22}{t^2-9t+20}\le 0 \iff \frac{t}{t-4}+\frac{t+5}{t-5}+\frac{22}{(t-4)(t-5)}\le 0 \iff$ $\iff \frac{t(t-5)+(t+5)(t-4)+22}{(t-4)(t-5)}\le 0 \iff \frac{t^2-5t+t^2-4t+5t-20+22}{(t-4)(t-5)}\le 0 \iff$ $\iff \frac{2t^2-4t+2}{(t-4)(t-5)}\le 0 \iff \frac{2(t-1)^2}{(t-4)(t-5)}\le 0.$

$\text{Решим полученное неравенство методом интервалов:}$

$\left[ \begin{aligned} &t=1,\\ &4<t<5 \end{aligned} \right. \iff \left[ \begin{aligned} &5^x=1,\\ &4<5^x<5 \end{aligned} \right. \iff \left[ \begin{aligned} &5^x=5^0,\\ &5^{\log_5 4}<5^x<5^1 \end{aligned} \right. \iff \left[ \begin{aligned} &x=0,\\ &\log_5 4<x<1. \end{aligned} \right.$

$\text{Таким образом, решен</article></body></html>$

Задание №30102 ЕГЭ по Математике