помогите решить неравенство, плиииз!!!!. Created by MariSar. matematika-ru

решаем методом интервалов_______ -√6/18________0_______√6/6_______ <0 >0 <0 >0делаем обратную заменурешений нет Знаменатель для любых а положителенОтвет [0;1]

помогите решить неравенство, плиииз!!!!...

MariSar @MariSar

July 2022 1 9 Report

помогите решить неравенство, плиииз!!!!

Answers & Comments

hote

Verified answer

$\displaystyle 9(1+5^{1-2x})^{-\frac{1}{2}}-\frac{1}{2}(5+5^{2x})^{\frac{1}{2}}\geq 6^{\frac{1}{2}}*(5^x)^{\frac{1}{2}}\\\\9(1+\frac{5}{5^{2x}})^{-\frac{1}{2}}-\frac{1}{2}(5+5^{2x})^{\frac{1}{2}}\geq \sqrt{6}*(5^x)^{\frac{1}{2}}\\\\9(\frac{5^{2x}}{5^{2x}+5})^{\frac{1}{2}}-\frac{1}{2}(5+5^{2x})^{\frac{1}{2}}\geq \sqrt{6}*(5^x)^{\frac{1}{2}}| : (5^x)^{\frac{1}{2}}\\\\9(\frac{5^x}{5^{2x}+5})^{\frac{1}{2}}-\frac{1}{2}(\frac{5+5^{2x}}{5^x})^{\frac{1}{2}}\geq \sqrt{6}$

$\displaystyle(\frac{5^x}{5^{2x}+5})^{\frac{1}{2}}=t$

$\displaystyle 9t-\frac{1}{2t}\geq \sqrt{6}\\\\\frac{18t^2-2\sqrt{6}t-1}{2t}\geq 0\\\\18t^2-2\sqrt{6}t-1=0\\\\D=4*6+4*18=96=(4\sqrt{6})^2\\\\t_{1.2}=\frac{2\sqrt{6}\pm 4\sqrt{6}}{36}\\\\t_1=\frac{\sqrt{6}}{6}; t_2=-\frac{\sqrt{6}}{18}$

$\displaystyle \frac{18(t-\frac{\sqrt{6}}{6})(t+\frac{\sqrt{6}}{18})}{2t}\geq 0$

решаем методом интервалов

_______ -√6/18________0_______√6/6_______

<0 >0 <0 >0

$\displaystyle -\frac{\sqrt{6}}{18}\leq t$

делаем обратную замену

$\displaystyle -\frac{\sqrt{6}}{18}\leq (\frac{5^x}{5^{2x}+5})^{\frac{1}{2}}$

решений нет

$\displaystyle (\frac{5^x}{5^{2x}+5})^\frac{1}{2}\geq\frac{\sqrt{6}}{6}\\\\\frac{5^x}{5^{2x}+5}\geq \frac{1}{6}\\\\\frac{6*5^x-5^{2x}-5}{6(5^{2x}+5)}\geq 0\\\\\ 5^x=a\\\\\frac{-(a^2-6a+5)}{6(a^2+5)}\geq 0$

Знаменатель для любых а положителен

$\displaystyle -(a^2-6a+5)\geq 0\\\\-(a-1)(a-5)\geq 0\\\\1\leq a\leq 5\\\\1\leq 5^x\leq 5\\\\0\leq x\leq 1$

Ответ [0;1]

5 votes Thanks 5

Answers & Comments

Verified answer

pomogite reshit pozhalujsta dayu 49 ballov97b7ff4c3f42ee7a63a101a44cd65dfa 14622

napishite podrobnoe reshenie pozhalujsta zadanie prilozheno

5 kak reshat s obyasneniempliz

izvestno chto summa pervyh dvuh chlenov geometricheskoj progressii ravna 48 a sum1e0f6b8bbb5851bf9a49441b3e027c66 16450

pomogite reshit podrobno pozhalujsta zadanie prilozheno

diagonal pryamougolnogo parallelepipeda ravna 13 a diagonali ego bokovyh grane

obyasnite kak reshat pozhalujsta zadanie prilozheno

obyasnite kak reshit pozhalujsta zadanie prilozheno

ch bolshe skorosti vtoroj reki podrobno pozhalujsta

tex predstavlyaet soboj rovno odnu tochku otvet zapishite desyatichnoj drobyu s zap

рекомендуемые вопросы

Helpful Links

Helpful Social