Question Number 64631 by Mikael last updated on 19/Jul/19 $$\sqrt{\frac{\mathrm{1}+\mathrm{2}{x}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{\mathrm{2}}}+\mathrm{2}{x}^{\mathrm{2}} =\mathrm{1} \\ $$$$\mathrm{To}\:\mathrm{solve}\:\mathrm{in}\:\mathbb{R} \\ $$ Commented by behi83417@gmail.com last updated on 20/Jul/19 $$−\mathrm{1}<\mathrm{x}\leqslant\mathrm{1},\mathrm{let}:\:\mathrm{x}=\mathrm{cost} \\…
Question Number 64604 by mathmax by abdo last updated on 19/Jul/19 $${find}\:\:{all}\:{integr}\:{naturals}\:{n}\:{and}\:{k}\:{wich}\:{verify} \\ $$$${k}!=\left(\mathrm{2}^{{n}} −\mathrm{1}\right)\left(\mathrm{2}^{{n}} −\mathrm{2}\right)\left(\mathrm{2}^{{n}} −\mathrm{4}\right)…\left(\mathrm{2}^{{n}} −\mathrm{2}^{{n}−\mathrm{1}} \right) \\ $$ Terms of Service Privacy…
Question Number 64580 by jimful last updated on 19/Jul/19 $${a}^{\mathrm{2}} +{b}^{\mathrm{2}} ={a}+{b}\:,{a}^{\mathrm{2}} −{b}^{\mathrm{2}} ={ab} \\ $$$${a}=?\:{b}=? \\ $$$${and}\:{what}\:{if}\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} ={a}−{b}? \\ $$ Answered by meme…
Question Number 130092 by Adel last updated on 22/Jan/21 Commented by 0731619177 last updated on 24/Jan/21 $${hhhh} \\ $$ Answered by Dwaipayan Shikari last updated…
Question Number 130089 by ajfour last updated on 22/Jan/21 $${To}\:{solve}\:\:\:{x}^{\mathrm{3}} ={x}+{c} \\ $$$${Let}\:\:{y}=\left({x}−{p}\right)\left({x}^{\mathrm{3}} −{x}−{c}\right) \\ $$$$\:\:\frac{{dy}}{{dx}}=\left({x}^{\mathrm{3}} −{x}−{c}\right)+\left(\mathrm{3}{x}^{\mathrm{2}} −\mathrm{1}\right)\left({x}−{p}\right) \\ $$$$\:\:{let}\:\:\:\frac{{dy}}{{dx}}={mx} \\ $$$$\Rightarrow\:\:\left(\mathrm{3}{x}^{\mathrm{2}} −\mathrm{1}\right)\left({x}−{p}\right)={mx} \\ $$$$\mathrm{3}{x}^{\mathrm{3}}…
Question Number 64542 by LPM last updated on 19/Jul/19 Answered by MJS last updated on 19/Jul/19 $${b}=\mathrm{1}−{a} \\ $$$${a}^{\mathrm{2}} +\left(\mathrm{1}−{a}\right)^{\mathrm{2}} =\mathrm{2}\:\Rightarrow\:{a}=\frac{\mathrm{1}}{\mathrm{2}}\pm\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\:\Rightarrow\:{b}=\frac{\mathrm{1}}{\mathrm{2}}\mp\frac{\sqrt{\mathrm{3}}}{\mathrm{2}} \\ $$$${a}^{\mathrm{7}} =\frac{\mathrm{71}}{\mathrm{16}}\pm\frac{\mathrm{41}\sqrt{\mathrm{3}}}{\mathrm{16}}\:\:\:{b}^{\mathrm{7}} =\frac{\mathrm{71}}{\mathrm{16}}\mp\frac{\mathrm{41}\sqrt{\mathrm{3}}}{\mathrm{16}}…
Question Number 64519 by necx1 last updated on 18/Jul/19 $${a},{b},{c}\:{is}\:{a}\:{geometric}\:{progression}\:{such} \\ $$$${that} \\ $$$${a}+{b}+{c}=\mathrm{26} \\ $$$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} =\mathrm{364} \\ $$$$ \\ $$$${find}\:{a},{b},{c} \\ $$…
Question Number 64508 by lalitchand last updated on 18/Jul/19 $$\mathrm{factorize}\:\left(\mathrm{x}+\mathrm{1}\right)\left(\mathrm{x}+\mathrm{3}\right)\left(\mathrm{x}+\mathrm{5}\right)\left(\mathrm{x}+\mathrm{7}\right)+\mathrm{16} \\ $$ Commented by Prithwish sen last updated on 18/Jul/19 $$\left(\mathrm{x}+\mathrm{1}\right)\left(\mathrm{x}+\mathrm{7}\right)\left(\mathrm{x}+\mathrm{3}\right)\left(\mathrm{x}+\mathrm{5}\right)+\mathrm{16} \\ $$$$=\left(\mathrm{x}^{\mathrm{2}} +\mathrm{8x}+\mathrm{7}\right)\left(\mathrm{x}^{\mathrm{2}} +\mathrm{8x}+\mathrm{15}\right)+\mathrm{16}…
Question Number 130036 by liberty last updated on 22/Jan/21 $$\mathrm{If}\:\begin{cases}{{a}+{b}+{c}\:=\:\mathrm{1}}\\{{a}^{\mathrm{3}} +{b}^{\mathrm{3}} +{c}^{\mathrm{3}} \:=\:\mathrm{4}}\end{cases} \\ $$$$\:\mathrm{find}\:\frac{\mathrm{1}}{{a}+{bc}}\:+\:\frac{\mathrm{1}}{{b}+{ca}}\:+\:\frac{\mathrm{1}}{{c}+{ab}}. \\ $$ Answered by mnjuly1970 last updated on 22/Jan/21 $${solution}:\:\left\{_{{a}^{\mathrm{3}}…
Question Number 64475 by aliesam last updated on 18/Jul/19 $${solve}\:{the}\:{equation} \\ $$$${sin}\left({x}\right)+{sin}\left(\mathrm{2}{x}\right)+{sin}\left(\mathrm{3}{x}\right)={cos}\left({x}\right)+{cos}\left(\mathrm{2}{x}\right)+{cos}\left(\mathrm{3}{x}\right) \\ $$ Commented by mathmax by abdo last updated on 18/Jul/19 $${let}\:{u}_{{n}} =\sum_{{k}=\mathrm{0}}…