Question Number 145238 by liberty last updated on 03/Jul/21 Answered by gsk2684 last updated on 03/Jul/21 $$\mathrm{x}=\mathrm{1}\:\mathrm{or}\:\frac{\mathrm{1}}{\mathrm{3}} \\ $$ Answered by Rasheed.Sindhi last updated on…
Question Number 145231 by mathdanisur last updated on 03/Jul/21 $$\mathrm{1}<{a}\leqslant{b}\:\:{then}\:{find} \\ $$$$\underset{\:\boldsymbol{{a}}} {\overset{\:\boldsymbol{{b}}} {\int}}\:{tan}^{-\mathrm{1}} \left(\frac{\mathrm{3}{x}}{\mathrm{1}-\mathrm{2}{x}^{\mathrm{2}} }\right){dx}=? \\ $$ Commented by Dwaipayan Shikari last updated on…
Question Number 145224 by mathdanisur last updated on 03/Jul/21 $$\sqrt{\mathrm{2}\sqrt{\mathrm{3}}\:+\:\mathrm{2}}\:-\:\sqrt{\sqrt{\mathrm{3}}\:-\:\sqrt{\mathrm{2}}}\:=\:? \\ $$ Answered by Olaf_Thorendsen last updated on 03/Jul/21 $$\left(\sqrt{\mathrm{3}}+\sqrt{\mathrm{2}}+\mathrm{1}\right)^{\mathrm{2}} \:=\:\mathrm{6}+\mathrm{2}\sqrt{\mathrm{6}}+\mathrm{2}\sqrt{\mathrm{3}}+\mathrm{2}\sqrt{\mathrm{2}} \\ $$$$ \\ $$$${x}\:=\:\sqrt{\mathrm{2}\sqrt{\mathrm{3}}+\mathrm{2}}−\sqrt{\sqrt{\mathrm{3}}−\sqrt{\mathrm{2}}}…
Question Number 14157 by b.e.h.i.8.3.4.1.7@gmail.com last updated on 29/May/17 Commented by ajfour last updated on 30/May/17 $${kindly}\:{view}\:{my}\:{solution}\:{in} \\ $$$${Q}.\mathrm{14306}\:{solved}\:{by}\:{coordinate} \\ $$$${geometry}.. \\ $$ Commented by…
Question Number 14147 by RasheedSindhi last updated on 28/May/17 $$\mathrm{Determine}: \\ $$$$\left({a}\right)\:\mathrm{e}^{\omega} \\ $$$$\left({b}\right)\:\omega^{\mathrm{e}} \\ $$ Commented by prakash jain last updated on 28/May/17 $${e}^{{w}}…
Question Number 14148 by RasheedSindhi last updated on 28/May/17 $$\mathrm{Determine} \\ $$$$\left({a}\right)\:{i}^{{i}} \\ $$$$\left({b}\right)\:\omega^{\omega} \\ $$$$\left({c}\right)\:{i}^{\omega} \\ $$$$\left({d}\right)\:\omega^{{i}} \\ $$ Answered by prakash jain last…
Question Number 145198 by loveineq last updated on 03/Jul/21 $$\mathrm{Let}\:{a}\geqslant{b}\geqslant{c}\geqslant\mathrm{0}\:,\:{c}^{\mathrm{3}} +\left({a}+{b}\right)^{\mathrm{3}} \neq\mathrm{0}\:\mathrm{and}\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} \:=\:\mathrm{3}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{2}}\:\leqslant\:\frac{{a}^{\mathrm{3}} +\left({b}+{c}\right)^{\mathrm{3}} +{b}^{\mathrm{3}} +\left({c}+{a}\right)^{\mathrm{3}} }{{c}^{\mathrm{3}} +\left({a}+{b}\right)^{\mathrm{3}} }\:\leqslant\:\mathrm{2} \\ $$$$\mathrm{Determine}\:\mathrm{when}\:\mathrm{equality}\:\mathrm{holds}.…
Question Number 145191 by mathdanisur last updated on 03/Jul/21 $${if}\:\:{q}\geqslant\mathrm{1}\:\:{and}\:\:{x}>−\mathrm{1}\:\:{then}: \\ $$$$\left(\mathrm{1}+{x}\right)^{\boldsymbol{{q}}} \:\geqslant\:\left(\mathrm{1}+{x}\right)^{\boldsymbol{{q}}−\mathrm{1}} \:+\:{x}\:\geqslant\:\mathrm{1}+{qx} \\ $$ Answered by Olaf_Thorendsen last updated on 03/Jul/21 $$\left(\mathrm{1}+{x}\right)^{{q}} \:=\:\left(\mathrm{1}+{x}\right)^{{q}−\mathrm{1}}…
Question Number 14119 by RasheedSindhi last updated on 28/May/17 $$\mathrm{For}\:\mathrm{what}\:\mathrm{values}\:\mathrm{of}\:\mathrm{n}\in\mathbb{N}, \\ $$$$\omega^{\mathrm{1}/\mathrm{n}} \:\mathrm{can}\:\mathrm{be}\:\mathrm{expressed}\:\mathrm{as}\:\omega^{\mathrm{m}} \\ $$$$\mathrm{where}\:\mathrm{m}\in\mathbb{Z}? \\ $$ Commented by prakash jain last updated on 28/May/17…
Question Number 14113 by FilupS last updated on 28/May/17 $$\mathrm{Is}\:\mathrm{this}\:\mathrm{incorrect}: \\ $$$${S}=\mathrm{2}×\mathrm{2}×… \\ $$$${S}=\mathrm{2}\left(\mathrm{2}×\mathrm{2}×…\right) \\ $$$${S}=\mathrm{2}{S} \\ $$$${S}=\mathrm{0} \\ $$$$\: \\ $$$$\mathrm{Please}\:\mathrm{explain}\:\mathrm{why} \\ $$ Commented…