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Question Number 211761 by MATHEMATICSAM last updated on 20/Sep/24 $$\mathrm{If}\:{x}\:=\:\frac{\mathrm{4}{a}^{\mathrm{2}} {b}}{\mathrm{4}{b}^{\mathrm{2}} \:+\:\mathrm{1}}\:\mathrm{where}\:{b}\:>\:\frac{\mathrm{1}}{\mathrm{2}}\:\mathrm{then} \\ $$$$\frac{\sqrt{{a}^{\mathrm{2}} \:+\:{x}}\:+\:\sqrt{{a}^{\mathrm{2}} \:−\:{x}}}{\:\sqrt{{a}^{\mathrm{2}} \:+\:{x}}\:−\:\sqrt{{a}^{\mathrm{2}} \:−\:{x}}}\:=\:? \\ $$ Answered by Rasheed.Sindhi last updated…
Question Number 211727 by Spillover last updated on 18/Sep/24 Answered by MrGaster last updated on 03/Nov/24 $$=\int_{−\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{4}}} \frac{\left(\pi−\mathrm{4}{x}\right)\mathrm{tan}\:{x}\left(\mathrm{1}+\mathrm{tan}\:{x}\right)}{\mathrm{1}−\mathrm{tan}^{\mathrm{2}} {x}}{dx} \\ $$$$=\int_{−\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{4}}} \frac{\left(\pi−\mathrm{4}{x}\right)\mathrm{tan}\:{x}+\left(\pi−\mathrm{4}{x}\right)\mathrm{tan}^{\mathrm{2}} {x}}{\mathrm{cos}^{\mathrm{2}}…
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Question Number 211722 by hardmath last updated on 18/Sep/24 $$\mathrm{a},\:\mathrm{b}\:\in\:\mathbb{N} \\ $$$$\mathrm{a}\:\centerdot\:\mathrm{b}\:=\:\mathrm{144} \\ $$$$ \\ $$how many different numbers can a and b be here?…
Question Number 211720 by Nadirhashim last updated on 18/Sep/24 $$\:\:\:\:\:\boldsymbol{{if}}\:\:\frac{\mathrm{8}^{\boldsymbol{{x}}} −\mathrm{2}^{\boldsymbol{{x}}} }{\mathrm{6}^{\boldsymbol{{x}}} −\mathrm{3}^{\boldsymbol{{x}}} }\:\:\:=\:\mathrm{2}\:\boldsymbol{{find}}\:\boldsymbol{{x}} \\ $$ Answered by Frix last updated on 18/Sep/24 $$\mathrm{obviously}\:{x}=\mathrm{1} \\…
Question Number 211719 by RojaTaniya last updated on 18/Sep/24 Commented by Frix last updated on 18/Sep/24 $${n}=\mathrm{1} \\ $$$$\mathrm{2}+\mathrm{12}+\mathrm{2011}=\mathrm{2025}=\mathrm{45}^{\mathrm{2}} \\ $$ Terms of Service Privacy…
Question Number 211706 by Nadirhashim last updated on 17/Sep/24 $$\:\:\:\:\:\boldsymbol{{if}}\:\:\boldsymbol{{x}}^{\boldsymbol{{log}}\mathrm{27}} +\:\:\:\mathrm{9}^{\boldsymbol{{logx}}} =\mathrm{36}\:\boldsymbol{{find}}\:\boldsymbol{{x}} \\ $$ Answered by mehdee7396 last updated on 17/Sep/24 $${x}^{\mathrm{3}{log}\mathrm{3}} +{x}^{\mathrm{2}{log}\mathrm{3}} =\mathrm{36}\:\: \\…
Question Number 211679 by MrGaster last updated on 16/Sep/24 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{Inverse}\:\mathrm{root}\:\mathrm{formula}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\boldsymbol{{x}}=\frac{\mathrm{2}\boldsymbol{{c}}}{−\boldsymbol{{b}}\pm\sqrt{\boldsymbol{{b}}^{\mathrm{2}} −\mathrm{4}\boldsymbol{{ac}}}} \\ $$$$\left(\mathrm{1}\right)\mathrm{The}“\:\mathrm{antiroot}\:\mathrm{formula}''\:\mathrm{is}\:\mathrm{derivedr} \\ $$$$\mathrm{fom}\:\mathrm{the}\:\mathrm{abovementionedt} \\ $$$$\mathrm{antiroo}\:\mathrm{formula}. \\ $$ Commented by…
Question Number 211673 by a.lgnaoui last updated on 16/Sep/24 $$\:\:\:\boldsymbol{{Resoudre}} \\ $$$$\:\:^{\boldsymbol{\mathrm{x}}} \sqrt{\frac{\boldsymbol{\mathrm{x}}}{\boldsymbol{\mathrm{x}}−\mathrm{1}}}\:\:\:=\left(\boldsymbol{\mathrm{x}}−\mathrm{1}\right)^{\left(\boldsymbol{\mathrm{x}}−\mathrm{2}\right)} . \\ $$ Answered by Frix last updated on 16/Sep/24 $$\mathrm{You}\:\mathrm{can}\:\mathrm{only}\:\mathrm{approximate} \\…