Question Number 43549 by peter frank last updated on 11/Sep/18 $${solve}\:{x}\::\:\left(\mathrm{5}+\mathrm{2}\sqrt{\mathrm{6}}\right)^{{x}^{\mathrm{2}} −\mathrm{3}} +\left(\mathrm{5}−\mathrm{2}\sqrt{\mathrm{6}}\right)^{{x}^{\mathrm{2}} −\mathrm{3}} =\mathrm{10} \\ $$ Commented by Cheyboy last updated on 12/Sep/18 $$\left(\mathrm{5}+\mathrm{2}\sqrt{\mathrm{6}}\right)\left(\mathrm{5}−\mathrm{2}\sqrt{\mathrm{6}}\right)\:=\:\mathrm{1}…
Question Number 43544 by behi83417@gmail.com last updated on 11/Sep/18 Answered by MJS last updated on 12/Sep/18 $${x}={z}−\frac{\mathrm{1}}{\mathrm{3}} \\ $$$${z}^{\mathrm{3}} −\frac{\mathrm{1}}{\mathrm{3}}{z}+\frac{\mathrm{2}}{\mathrm{27}}−\frac{\sqrt{\mathrm{2}}}{\mathrm{10}}=\mathrm{0} \\ $$$$\mathrm{trigonometric}\:\mathrm{solution}\:\mathrm{method} \\ $$$${z}_{{k}} =\mathrm{2}\sqrt{−\frac{{p}}{\mathrm{3}}}\mathrm{sin}\left(\frac{\mathrm{2}\pi{k}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{3}}\mathrm{arcsin}\left(\frac{\mathrm{9}{q}}{\mathrm{2}{p}^{\mathrm{2}}…
Question Number 43540 by abdo.msup.com last updated on 11/Sep/18 $${prove}\:{that}\:\mathrm{111}\:{divide}\:\mathrm{10}^{\mathrm{6}{n}+\mathrm{2}} \:+\mathrm{10}^{\mathrm{3}{n}+\mathrm{1}} \:+\mathrm{1} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 12/Sep/18 $$\mathrm{10}^{\mathrm{6}{n}} ×\mathrm{100}+\mathrm{10}^{\mathrm{3}{n}} ×\mathrm{10}+\mathrm{1} \\…
Question Number 109063 by mr W last updated on 20/Aug/20 Commented by mr W last updated on 20/Aug/20 $${see}\:{Q}\mathrm{107696} \\ $$ Terms of Service Privacy…
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Question Number 174587 by bekzodjumayev last updated on 05/Aug/22 Commented by kaivan.ahmadi last updated on 05/Aug/22 $${f}\left(−{x}\right)=−{f}\left({x}\right) \\ $$$$\Rightarrow{f}\:{is}\:{an}\:{odd}\:{function} \\ $$$$\Rightarrow{f}'\left({x}\right)={f}'\left(−{x}\right)\Rightarrow{f}'\:{is}\:{an}\:{even}\:{function} \\ $$$$\Rightarrow{fof}\left(−{x}\right)={f}\left(−{f}\left({x}\right)\right)=−{fof}\left({x}\right) \\ $$$$\Rightarrow{fof}\:{is}\:{an}\:{odd}\:{function}…
Question Number 174579 by behi834171 last updated on 04/Aug/22 $$\:\:\:\:{find}\:{minimum}\:{value}\:{of}: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\frac{\boldsymbol{{a}}^{\mathrm{2}} \left(\boldsymbol{{b}}−\mathrm{1}\right)^{\mathrm{2}} +\mathrm{2}\boldsymbol{{ab}}+\left(\boldsymbol{{a}}−\mathrm{1}\right)^{\mathrm{2}} }{\boldsymbol{{a}}\left(\boldsymbol{{ab}}+\mathrm{1}\right)}\:\:\:\:\:\:\:\:\:\left[\boldsymbol{{all}}\in\boldsymbol{{R}}\right] \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 174569 by behi834171 last updated on 04/Aug/22 $$\:\:\:\:\:\begin{cases}{\boldsymbol{{x}}+\boldsymbol{{z}}=\mathrm{0}}\\{\boldsymbol{{y}}+\boldsymbol{{t}}+\boldsymbol{{xz}}=−\mathrm{2}\boldsymbol{{b}}}\\{\boldsymbol{{xt}}+\boldsymbol{{yz}}=\mathrm{1}}\\{\boldsymbol{{yt}}=\boldsymbol{{b}}^{\mathrm{2}} −\boldsymbol{{a}}}\end{cases}\:\:\:\:\:\:\left[\:\:\boldsymbol{{all}}\in\boldsymbol{{R}}\right] \\ $$$$\boldsymbol{{solve}}\:\boldsymbol{{for}}\:\:\::\:\:\:\boldsymbol{{x}},\:\boldsymbol{{y}}\:,\boldsymbol{{z}},\:\boldsymbol{{t}}\:\:\:\:\:\:\:\:\:\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 174568 by AgniMath last updated on 04/Aug/22 $$\mathrm{If}\:\frac{\mathrm{1}}{{a}}\:+\:\frac{\mathrm{1}}{{b}}\:+\:\frac{\mathrm{1}}{{c}}\:=\:\frac{\mathrm{1}}{{a}\:+\:{b}\:+\:{c}}\:\mathrm{then}\: \\ $$$$\frac{\mathrm{1}}{{a}^{\mathrm{3}} }\:+\:\frac{\mathrm{1}}{{b}^{\mathrm{3}} \:}\:+\:\frac{\mathrm{1}}{{c}^{\mathrm{3}} }\:=\:? \\ $$ Answered by behi834171 last updated on 04/Aug/22 $$\boldsymbol{{impossible}}\:\boldsymbol{{to}}\:\boldsymbol{{find}}.…
Question Number 43496 by LYCON TRIX last updated on 11/Sep/18 $$\sqrt{\mathrm{a}−\sqrt{\mathrm{a}+\mathrm{x}}}\:\:+\:\:\sqrt{\mathrm{a}+\sqrt{\mathrm{a}−\mathrm{x}}}\:\:=\mathrm{2x}\: \\ $$$$\mathrm{Solve}\:\mathrm{for}\:“\:\mathrm{x}\:''\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\:“\:\:\mathrm{a}\:\:'' \\ $$$$ \\ $$ Commented by LYCON TRIX last updated on 11/Sep/18…