Question

помогите решить неравенство пожалуйста, подробнее​

Answer 1

Ответ:

х є {0} U ($log_{5}4$;1)

Объяснение:

$\frac{5^{x}}{5^{x}-4}+\frac{5^{x}+5}{5^{x}-5}+\frac{22}{25^{x}-9*5^{x}+20}\leq 0\\\\\frac{5^{x}(5^{x}-5)+(5^{x}+5)(5^{x}-4)+22}{(5^{x}-4)(5^{x}-5)}\leq 0\\\\\frac{5^{2x}-5*5^{x}+5^{2x}-4*5^{x}+5*5^{x}-20+22}{(5^{x}-4)(5^{x}-5)} \leq 0\\\\\frac{2*5^{2x}-4*5^{x}+2}{(5^{x}-4)(5^{x}-5)} \leq 0\\\\\frac{2(5^{x}-1)^2}{(5^{x}-4)(5^{x}-5)} \leq 0\\\\(5^{x}-1)^{2}\leq 0$

$\left \{ {{5^{x}-1\leq 0} \atop {5^{x}-1\geq 0}} \right. \\x=0\\\\\left \{ {{5^{x}-4\neq 0} \atop {5^{x}-5\neq 0}} \right. \\x\neq log_{5}4\\x\neq 1$

х є {0} U ($log_{5}4$;1)