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:T6b5, $\frac{2\cdot 8^{x-1}}{2\cdot 8^{x-1}-1}\ge \frac{3}{8^x-1}+\frac{8}{64^x-5\cdot 8^x+4} \iff \frac{\frac14\cdot 8^x}{\frac14\cdot 8^x-1}\ge \frac{3}{8^x-1}+\frac{8}{8^{2x}-5\cdot 8^x+4}.$

$\text{Пусть } 8^x=t. \text{ Тогда неравенство примет вид:}$

$\frac{t}{t-4}-\frac{3}{t-1}-\frac{8}{t^2-5t+4}\ge 0 \iff \frac{t}{t-4}-\frac{3}{t-1}-\frac{8}{(t-4)(t-1)}\ge 0 \iff$ $\iff \frac{t^2-t-3t+12-8}{(t-4)(t-1)}\ge 0 \iff \frac{t^2-4t+4}{(t-4)(t-1)}\ge 0 \iff \frac{(t-2)^2}{(t-4)(t-1)}\ge 0.$

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

$\left[ \begin{aligned} &t<1,\\ &t=2,\\ &t>4 \end{aligned} \right. \iff \left[ \begin{aligned} &8^x<1,\\ &8^x=2,\\ &8^x>4 \end{aligned} \right. \iff \left[ \begin{aligned} &8^x<8^0,\\ &2^{3x}=2^1,\\ &2^{3x}>2^2 \end{aligned} \right. \iff \left[ \begin{aligned} &x<0,\\ &x=\frac13,\\ &x>\frac23. \end{aligned} \right.$

$\text{Т</article></body></html>$

Задание №30103 ЕГЭ по Математике