Menu Close

Author: Tinku Tara

Question-194455

Question Number 194455 by Spillover last updated on 07/Jul/23 Answered by qaz last updated on 07/Jul/23 $$\frac{{x}^{\mathrm{4}} }{\mathrm{1}+{x}^{\mathrm{3}} }=\frac{{x}^{\mathrm{4}} }{{x}^{\mathrm{5}} +{x}^{\mathrm{3}} }=\frac{{x}}{\mathrm{1}+{x}^{\mathrm{2}} }\:\:\:\:\:\:\:,\frac{{x}^{\mathrm{3}} }{\mathrm{1}+{x}}=\frac{{x}^{\mathrm{3}} }{{x}^{\mathrm{5}}…

If-a-b-c-gt-0-such-that-a-b-c-3-prove-that-1-1-ab-1-1-ac-1-1-bc-9-2-a-b-c-

Question Number 194448 by York12 last updated on 07/Jul/23 $${If}\:{a}\:,\:{b}\:,\:{c}\:>\mathrm{0}\:,\:{such}\:{that}\:{a}+{b}+{c}=\mathrm{3} \\ $$$${prove}\:{that} \\ $$$$\frac{\mathrm{1}}{\mathrm{1}+{ab}}+\frac{\mathrm{1}}{\mathrm{1}+{ac}}+\frac{\mathrm{1}}{\mathrm{1}+{bc}}\geqslant\frac{\mathrm{9}}{\mathrm{2}\left(\sqrt{{a}}+\sqrt{{b}}+\sqrt{{c}}\right)} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Given-f-x-x-2-5x-a-x-gt-1-3x-2-x-b-x-1-if-f-x-passes-through-at-point-2-4-and-lim-x-1-f-x-exist-find-the-value-of-3a-2b-

Question Number 194429 by horsebrand11 last updated on 06/Jul/23 $$\:\:\mathrm{Given}\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\begin{cases}{\mathrm{x}^{\mathrm{2}} −\mathrm{5x}+\mathrm{a}\:;\:\mathrm{x}>\mathrm{1}}\\{\frac{\mathrm{3x}+\mathrm{2}}{\mathrm{x}−\mathrm{b}}\:;\:\mathrm{x}\leqslant\mathrm{1}}\end{cases} \\ $$$$\:\:\mathrm{if}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{passes}\:\mathrm{through}\:\mathrm{at}\:\mathrm{point}\: \\ $$$$\:\:\left(\mathrm{2},−\mathrm{4}\right)\:\mathrm{and}\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{exist}\:,\:\mathrm{find} \\ $$$$\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{3a}+\mathrm{2b}.\: \\ $$ Answered by MM42 last updated…

Question-194444

Question Number 194444 by Abdullahrussell last updated on 06/Jul/23 Answered by Frix last updated on 08/Jul/23 $$\mathrm{Let}\:{y}={px}\wedge{z}={qx} \\ $$$$\mathrm{It}'\mathrm{s}\:\mathrm{easy}\:\mathrm{to}\:\mathrm{get} \\ $$$${p}=\frac{{b}\left(\mathrm{4}−{b}\right)}{{ab}−\mathrm{2}\left({a}+{b}+{c}−\mathrm{4}\right)} \\ $$$${q}=\frac{{bc}−\mathrm{2}\left({a}+{b}+{c}−\mathrm{4}\right)}{{ab}−\mathrm{2}\left({a}+{b}+{c}−\mathrm{4}\right)} \\ $$$${ab}−\mathrm{2}\left({a}+{b}+{c}−\mathrm{4}\right)\neq\mathrm{0}…