Menu Close

Category: Arithmetic

Question-167955

Question Number 167955 by peter frank last updated on 30/Mar/22 Answered by JDamian last updated on 30/Mar/22 $$\mathrm{6}^{\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{1}} }+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{3}} }+\centerdot\centerdot\centerdot} =\mathrm{6}^{\mathrm{1}} =\mathrm{6} \\ $$…

Question-167867

Question Number 167867 by cortano1 last updated on 28/Mar/22 Commented by cortano1 last updated on 28/Mar/22 $$\:{How}\:\frac{\sqrt[{\mathrm{3}}]{\sqrt[{\mathrm{3}}]{{x}−\mathrm{2}}\:+\mathrm{2}}}{\:\sqrt[{\mathrm{3}}]{\mathrm{2}−\sqrt[{\mathrm{3}}]{{x}+\mathrm{2}}}}\:=\:\frac{\mathrm{2}}{\:\sqrt[{\mathrm{3}}]{\mathrm{2}−\sqrt[{\mathrm{3}}]{{x}+\mathrm{2}}}} \\ $$ Commented by MJS_new last updated on…

Question-167776

Question Number 167776 by peter frank last updated on 24/Mar/22 Answered by MikeH last updated on 24/Mar/22 $${ax}^{\mathrm{2}} +{bx}\:+{c}\:=\:{a}\left({x}^{\mathrm{2}} +\frac{{b}}{{a}}{x}\:+\:\frac{{c}}{{a}}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:{a}\left[\left({x}+\frac{{b}}{\mathrm{2}{a}}\right)^{\mathrm{2}} −\frac{{b}^{\mathrm{2}} }{\mathrm{4}{a}^{\mathrm{2}} }+\frac{{c}}{{a}}\right]…

Question-36576

Question Number 36576 by ast empire last updated on 03/Jun/18 Commented by prof Abdo imad last updated on 03/Jun/18 $${let}\:{put}\:{A}\:=\:\frac{{x}^{\mathrm{100}} }{\mathrm{1}+{x}+{x}^{\mathrm{2}} \:+….+{x}^{\mathrm{200}} } \\ $$$${if}\:{x}=\mathrm{1}\:\:\:{A}\:=\:\frac{\mathrm{1}}{\mathrm{201}}…

Question-167609

Question Number 167609 by peter frank last updated on 20/Mar/22 Answered by MJS_new last updated on 20/Mar/22 $$\int\frac{\mathrm{1}−{x}^{\mathrm{2}} }{\left({x}−\mathrm{2}{x}^{\mathrm{2}} \right)}{dx}=\int\left(\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{{x}}−\frac{\mathrm{3}}{\mathrm{2}\left(\mathrm{2}{x}−\mathrm{1}\right)}\right){dx}= \\ $$$$=\frac{{x}}{\mathrm{2}}+\mathrm{ln}\:\mid{x}\mid\:−\frac{\mathrm{3}}{\mathrm{4}}\mathrm{ln}\:\mid\mathrm{2}{x}−\mathrm{1}\mid\:+{C} \\ $$ Commented…

Find-out-a-b-c-where-a-2-b-2-c-2-a-b-c-1000-

Question Number 167533 by cortano1 last updated on 19/Mar/22 $$\:\:\:\:\:\:\mathrm{Find}\:\mathrm{out}\:\mathrm{a},\mathrm{b},\mathrm{c}\:\mathrm{where}\:\begin{cases}{\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} =\mathrm{c}^{\mathrm{2}} }\\{\mathrm{a}+\mathrm{b}+\mathrm{c}=\mathrm{1000}}\end{cases}\:\:\: \\ $$ Commented by Rasheed.Sindhi last updated on 19/Mar/22 $$\mathrm{a},\mathrm{b},\mathrm{c}\in\mathbb{N}\:{or}\:\mathrm{a},\mathrm{b},\mathrm{c}\in\mathbb{Z}\:? \\ $$…