Question Number 4679 by 314159 last updated on 22/Feb/16 $${Let}\:{a},{b},{c},{d}\:\in{R}\:,{a}+{b}+{c}+{d}=\mathrm{0}.{Prove}\:{that} \\ $$$$\underset{{cyc}} {\sum}\left(\frac{\mathrm{1}}{\:\sqrt{{a}^{\mathrm{2}} +{a}+\mathrm{1}}}\right)\leqslant\mathrm{4}. \\ $$ Commented by prakash jain last updated on 21/Feb/16 $$\mathrm{It}\:\mathrm{is}\:\mathrm{not}\:\mathrm{much}\:\mathrm{less}\:\mathrm{than}\:\mathrm{4}.…
Question Number 135744 by liberty last updated on 15/Mar/21 $$ \\ $$Shabbat Shalom~ As Passover approaches What are you in bondage from? Don’t blame others,…
Question Number 4674 by thachan last updated on 20/Feb/16 $${x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{2}=\mathrm{0} \\ $$ Answered by FilupSmith last updated on 20/Feb/16 $${x}=\frac{−{b}\pm\sqrt{{b}^{\mathrm{2}} −\mathrm{4}{ac}}}{\mathrm{2}{a}} \\ $$$${x}=\frac{−\mathrm{5}\pm\sqrt{\mathrm{25}−\mathrm{4}\left(\mathrm{1}\right)\left(\mathrm{2}\right)}}{\mathrm{2}\left(\mathrm{1}\right)} \\…
Question Number 135747 by liberty last updated on 15/Mar/21 $$ \\ $$To make the ellipse 4𝑥^2 + 𝑦^2 + 𝑎𝑥 + 𝑏𝑦 + 𝑐 =…
Question Number 4671 by 314159 last updated on 20/Feb/16 $${Define}\:{a}\:{function}\:{f}:{R}\rightarrow{R}\:{such}\:{that}\:{f}\left({f}\left({x}\right)\right)={x}^{\mathrm{2}} −{x}+\mathrm{1} \\ $$$${for}\:{all}\:{real}\:{x}.{Evaluate}\:{f}\left(\mathrm{0}\right). \\ $$$$ \\ $$ Answered by 123456 last updated on 20/Feb/16 $${f}\left({f}\left({x}\right)\right)={x}^{\mathrm{2}}…
Question Number 4670 by malwaan last updated on 20/Feb/16 $${prove}\:{that} \\ $$$$\mathrm{0}.\mathrm{101101110}\rightarrow\: \\ $$$${irrational}\:{number} \\ $$ Commented by prakash jain last updated on 21/Feb/16 $$\mathrm{Non}−\mathrm{recurring}\:\mathrm{non}−\mathrm{terminating}\:\mathrm{decimals}…
Question Number 135742 by mohssinee last updated on 15/Mar/21 Commented by mohssinee last updated on 15/Mar/21 $${help}\:{me}\:! \\ $$ Answered by mathmax by abdo last…
Question Number 4668 by FilupSmith last updated on 20/Feb/16 $${S}=\underset{{i}=\mathrm{1}} {\overset{\infty} {\sum}}\:^{{i}} \sqrt{{n}},\:\:\:{n}\in\mathbb{R} \\ $$$$\mathrm{Can}\:{S}\:\mathrm{be}\:\mathrm{solved}? \\ $$ Answered by Yozzii last updated on 20/Feb/16 $${S}\left({N}\right)=\underset{{i}=\mathrm{1}}…
Question Number 135737 by Ar Brandon last updated on 15/Mar/21 $$\int_{−\mathrm{2}\pi} ^{\mathrm{4}\pi} \frac{\mathrm{3}}{\mathrm{5}−\mathrm{4cosx}}\mathrm{dx} \\ $$ Answered by mathmax by abdo last updated on 15/Mar/21 $$\Phi=\int_{−\mathrm{2}\pi}…
Question Number 70198 by smartsmith459@gmail.com last updated on 01/Oct/19 Answered by MJS last updated on 01/Oct/19 $${x}={a}^{\sqrt{\mathrm{log}_{{a}} \:{b}}} \\ $$$$\mathrm{ln}\:{x}\:=\sqrt{\frac{\mathrm{ln}\:{b}}{\mathrm{ln}\:{a}}}\mathrm{ln}\:{a}\:=\sqrt{\mathrm{ln}\:{a}\:×\mathrm{ln}\:{b}} \\ $$$$\Rightarrow\:\mathrm{5}^{\sqrt{\mathrm{log}_{\mathrm{5}} \:\mathrm{7}}} −\mathrm{7}^{\sqrt{\mathrm{log}_{\mathrm{7}} \:\mathrm{5}}}…