Question Number 167776 by peter frank last updated on 24/Mar/22 Answered by MikeH last updated on 24/Mar/22 $${ax}^{\mathrm{2}} +{bx}\:+{c}\:=\:{a}\left({x}^{\mathrm{2}} +\frac{{b}}{{a}}{x}\:+\:\frac{{c}}{{a}}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:{a}\left[\left({x}+\frac{{b}}{\mathrm{2}{a}}\right)^{\mathrm{2}} −\frac{{b}^{\mathrm{2}} }{\mathrm{4}{a}^{\mathrm{2}} }+\frac{{c}}{{a}}\right]…
Question Number 167775 by peter frank last updated on 24/Mar/22 Commented by infinityaction last updated on 24/Mar/22 $${put}\:{x}^{\mathrm{4}\:} \:={t} \\ $$ Answered by peter frank…
Question Number 36576 by ast empire last updated on 03/Jun/18 Commented by prof Abdo imad last updated on 03/Jun/18 $${let}\:{put}\:{A}\:=\:\frac{{x}^{\mathrm{100}} }{\mathrm{1}+{x}+{x}^{\mathrm{2}} \:+….+{x}^{\mathrm{200}} } \\ $$$${if}\:{x}=\mathrm{1}\:\:\:{A}\:=\:\frac{\mathrm{1}}{\mathrm{201}}…
Question Number 167609 by peter frank last updated on 20/Mar/22 Answered by MJS_new last updated on 20/Mar/22 $$\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…
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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 $$\mathrm{a},\mathrm{b},\mathrm{c}\in\mathbb{N}\:{or}\:\mathrm{a},\mathrm{b},\mathrm{c}\in\mathbb{Z}\:? \\ $$…
Question Number 101974 by Ari last updated on 05/Jul/20 Commented by prakash jain last updated on 05/Jul/20 $$\mathrm{Can}\:\mathrm{you}\:\mathrm{please}\:\mathrm{attach}\:\mathrm{image}\:\mathrm{to}\:\mathrm{this} \\ $$$$\mathrm{question}.\:\mathrm{There}\:\mathrm{is}\:\mathrm{an}\:\mathrm{option}\:\mathrm{to} \\ $$$$\mathrm{attach}\:\mathrm{image} \\ $$ Answered…
Question Number 167334 by cortano1 last updated on 13/Mar/22 $$\:\:\:\:{b}^{{b}} .\mathrm{2}^{{b}^{{b}^{\mathrm{2}} } } \:=\:\mathrm{4}\:\Rightarrow{b}=? \\ $$ Answered by MJS_new last updated on 13/Mar/22 $${b}\approx\mathrm{1}.\mathrm{28966784838} \\…
Question Number 101779 by I want to learn more last updated on 04/Jul/20 $$\mathrm{If}\:\:\:\:\mathrm{S}_{\mathrm{n}} \:\:\mathrm{is}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{first}\:\:\mathrm{n}\:\:\mathrm{terms}\:\mathrm{of}\:\mathrm{an}\:\mathrm{A}.\mathrm{P}. \\ $$$$\mathrm{Express}\:\:\:\mathrm{S}_{\mathrm{2k}} \:\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\:\:\mathrm{S}_{\mathrm{k}} \:\:\mathrm{and}\:\:\:\mathrm{S}_{\mathrm{3k}} \\ $$ Answered by bemath last…
Question Number 36163 by bshahid010@gmail.com last updated on 29/May/18 Commented by abdo mathsup 649 cc last updated on 29/May/18 $${let}\:{put}\:\:{A}_{{n}} =\:\prod_{{k}=\mathrm{2}} ^{{n}} \:\left(\:\:\mathrm{1}\:−\frac{\mathrm{1}}{{k}^{\mathrm{2}} }\right) \\…