Question Number 83834 by Power last updated on 06/Mar/20 Commented by niroj last updated on 06/Mar/20 $$\:\:\int\:\frac{\:\:\mathrm{1}}{\:\sqrt{\mathrm{x}\left(\mathrm{a}−\mathrm{x}\right)}}\mathrm{dx} \\ $$$$\:=\:\int\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{ax}−\mathrm{x}^{\mathrm{2}} }}\mathrm{dx}=\:\int\:\frac{\:\mathrm{1}}{\:\sqrt{−\left(\mathrm{x}^{\mathrm{2}} −\mathrm{2x}.\frac{\mathrm{a}}{\mathrm{2}}+\frac{\mathrm{a}^{\mathrm{2}} }{\mathrm{4}}−\frac{\mathrm{a}^{\mathrm{2}} }{\mathrm{4}}\right)}}\mathrm{dx} \\ $$$$\:=\:\int\:\frac{\mathrm{1}}{\:\sqrt{−\left[\left(\mathrm{x}−\frac{\mathrm{a}}{\mathrm{2}}\right)^{\mathrm{2}}…
Question Number 18299 by tawa tawa last updated on 18/Jul/17 $$\mathrm{x}^{\mathrm{x}^{\mathrm{x}} } \:=\:\mathrm{2},\:\:\:\:\:\:\mathrm{find}\:\:\mathrm{x} \\ $$ Commented by mrW1 last updated on 19/Jul/17 $$\mathrm{no}\:\mathrm{analytic}\:\mathrm{solution} \\ $$$$\sqrt{\mathrm{2}}<\mathrm{x}<\mathrm{2}…
Question Number 83822 by Power last updated on 06/Mar/20 Commented by mathmax by abdo last updated on 07/Mar/20 $${I}\:=\int\:\:\frac{{dx}}{\:\sqrt{\mathrm{2}{x}−\mathrm{1}}−^{\mathrm{4}} \sqrt{\mathrm{2}{x}−\mathrm{1}}}\:{cha}\mathrm{7}{gement}\:\:^{\mathrm{4}} \sqrt{\mathrm{2}{x}−\mathrm{1}}={t}\:{give} \\ $$$$\mathrm{2}{x}−\mathrm{1}\:={t}^{\mathrm{4}} \:\Rightarrow\mathrm{2}{x}=\mathrm{1}+{t}^{\mathrm{4}} \:\Rightarrow\:\mathrm{2}{dx}\:=\mathrm{4}{t}^{\mathrm{3}}…
Question Number 83824 by Power last updated on 06/Mar/20 Commented by mathmax by abdo last updated on 06/Mar/20 $${changement}\:{x}=\frac{\pi}{\mathrm{2}}−{t}\:{give} \\ $$$$\Omega\:=−\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{\pi\left(\frac{\pi}{\mathrm{2}}−{t}\right)+{cos}^{\mathrm{4}} {t}−{sin}^{\mathrm{4}} {t}}{{cos}^{\mathrm{4}}…
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Question Number 149354 by mathdanisur last updated on 04/Aug/21 $${z}>\mathrm{0} \\ $$$${z}^{\mathrm{2}} \:+\:\mathrm{12}\sqrt{{z}}\:=\:\mathrm{5} \\ $$$${z}\:+\:\mathrm{2}\sqrt{{z}}\:=\:? \\ $$ Commented by Rasheed.Sindhi last updated on 05/Aug/21 $$\smile\frown\smile\frown\smile\frown\smile\frown\smile\frown\smile\frown\smile\frown\smile…
Question Number 149331 by Samimsultani last updated on 04/Aug/21 Commented by john_santu last updated on 04/Aug/21 $$\mathrm{may}\:\mathrm{be}\:\mathrm{x}=\sqrt[{\mathrm{3}}]{\mathrm{7}+\sqrt{\mathrm{5}}}\:−\sqrt[{\mathrm{3}}]{\mathrm{7}−\sqrt{\mathrm{5}}}\: \\ $$ Commented by amin96 last updated on…
Question Number 83787 by john santu last updated on 06/Mar/20 $$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{abc}\:\mathrm{if}\: \\ $$$$\sqrt{\mathrm{2}+\sqrt{\mathrm{2}^{\mathrm{2}} +\sqrt{\mathrm{2}^{\mathrm{3}} +\mathrm{2}^{\mathrm{4}} +\sqrt{…}}}}\:=\:\frac{\sqrt{\mathrm{a}}+\sqrt{\mathrm{b}}}{\mathrm{c}} \\ $$ Answered by jagoll last updated on 06/Mar/20…
Question Number 83791 by jagoll last updated on 06/Mar/20 $$\mathrm{Let}\:\mathrm{x},\:\mathrm{y}\:\mathrm{are}\:\mathrm{two}\:\mathrm{different}\:\mathrm{real} \\ $$$$\mathrm{numbers}\:\mathrm{satisfy}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$$\sqrt{\mathrm{y}+\mathrm{4}}\:=\:\mathrm{x}−\mathrm{4}\:\mathrm{and}\:\sqrt{\mathrm{x}+\mathrm{4}}\:=\:\mathrm{y}−\mathrm{4}. \\ $$$$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}^{\mathrm{3}} +\mathrm{y}^{\mathrm{3}} \:\mathrm{mod}\left(\mathrm{x}^{\mathrm{3}} \mathrm{y}^{\mathrm{3}} \right)\:\mathrm{is} \\ $$ Commented by mr…
Question Number 149322 by mathdanisur last updated on 04/Aug/21 $$\frac{\underset{\boldsymbol{{n}}=\mathrm{1}} {\overset{\mathrm{99}} {\sum}}\left(\sqrt{\mathrm{10}\:+\:\sqrt{\boldsymbol{{n}}}}\right)}{\underset{\boldsymbol{{n}}=\mathrm{1}} {\overset{\mathrm{99}} {\sum}}\left(\sqrt{\mathrm{10}\:-\:\sqrt{\boldsymbol{{n}}}}\right)}\:=\:? \\ $$ Commented by amin96 last updated on 04/Aug/21 $$? \\…