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Category: Algebra

2x-1-1-3-x-1-1-3-1-

Question Number 68768 by aliesam last updated on 15/Sep/19 $$\sqrt[{\mathrm{3}}]{\mathrm{2}{x}−\mathrm{1}}\:+\sqrt[{\mathrm{3}}]{{x}−\mathrm{1}}\:=\:\mathrm{1} \\ $$ Commented by kaivan.ahmadi last updated on 15/Sep/19 $${t}={x}−\mathrm{1}\Rightarrow{x}={t}+\mathrm{1}\Rightarrow \\ $$$$\sqrt[{\mathrm{3}}]{\mathrm{2}{t}+\mathrm{1}}+\sqrt[{\mathrm{3}}]{{t}}=\mathrm{1}\Rightarrow\sqrt[{\mathrm{3}}]{\mathrm{2}{t}+\mathrm{1}}=\mathrm{1}−\sqrt[{\mathrm{3}}]{{t}}\Rightarrow \\ $$$$\mathrm{2}{t}+\mathrm{1}=\mathrm{1}−\mathrm{3}\sqrt[{\mathrm{3}}]{{t}}+\mathrm{3}\sqrt[{\mathrm{3}}]{{t}^{\mathrm{2}} }−{t}\Rightarrow\mathrm{3}{t}=\mathrm{3}\sqrt[{\mathrm{3}}]{{t}}\left(\sqrt[{\mathrm{3}}]{{t}}−\mathrm{1}\right)\Rightarrow…

Question-134297

Question Number 134297 by mathlove last updated on 02/Mar/21 Answered by Ñï= last updated on 02/Mar/21 $$\frac{{d}}{{dx}}{ln}\left({x}^{{x}} +\mathrm{2}^{{x}^{{x}} } \right)=\frac{\mathrm{1}}{{x}^{{x}} +\mathrm{2}^{{x}^{{x}} } }\left[{x}^{{x}} \left({lnx}+\mathrm{1}\right)+\left({ln}\mathrm{2}\right)\mathrm{2}^{{x}^{{x}} }…

Prove-that-ratio-of-circles-perimeter-to-its-radius-is-constant-Proof-should-not-utilize-a-result-based-on-the-above-fact-

Question Number 3215 by prakash jain last updated on 07/Dec/15 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{circles}\:\mathrm{perimeter}\:\mathrm{to} \\ $$$$\mathrm{its}\:\mathrm{radius}\:\mathrm{is}\:\mathrm{constant}. \\ $$$$\mathrm{Proof}\:\mathrm{should}\:\mathrm{not}\:\mathrm{utilize}\:\mathrm{a}\:\mathrm{result}\:\mathrm{based} \\ $$$$\mathrm{on}\:\mathrm{the}\:\mathrm{above}\:\mathrm{fact}. \\ $$ Answered by Yozzi last updated on…

Question-68740

Question Number 68740 by ahmadshah last updated on 15/Sep/19 Commented by Prithwish sen last updated on 15/Sep/19 $$\sqrt{\mathrm{30}\sqrt{\mathrm{30}\sqrt{\mathrm{30}\sqrt{\mathrm{30}}\sqrt{\mathrm{30}\left(\mathrm{30}^{\mathrm{2}} \right)^{\frac{\mathrm{1}}{\mathrm{2}}} }}}} \\ $$$$=\sqrt{\mathrm{30}\sqrt{\mathrm{30}\sqrt{\mathrm{30}\sqrt{\mathrm{30}}\sqrt{\left(\mathrm{30}\right)^{\mathrm{2}} }}}} \\ $$$$=\sqrt{\mathrm{30}\sqrt{\mathrm{30}\sqrt{\left(\mathrm{30}\right)^{\frac{\mathrm{5}}{\mathrm{2}}}…