Question Number 733 by 123456 last updated on 05/Mar/15 $$\mid\mid\mid\mid\mid\mid\mid{x}^{\mathrm{2}} −{x}−\mathrm{1}\mid−\mathrm{3}\mid−\mathrm{5}\mid−\mathrm{7}\mid−\mathrm{9}\mid−\mathrm{11}\mid−\mathrm{13}\mid \\ $$$$={x}^{\mathrm{2}} −\mathrm{2}{x}−\mathrm{48} \\ $$$${find}\:{all}\:{x}\:{real}\:{that}\:{is}\:{solution}\:{of}\:{above} \\ $$$${equation} \\ $$ Answered by prakash jain last…
Question Number 698 by 9999 last updated on 01/Mar/15 $${solve}\:{for}\:{x} \\ $$$$\frac{{a}}{{ax}−\mathrm{1}}+\frac{{b}}{{bx}−\mathrm{1}}={a}+{b} \\ $$ Commented by 123456 last updated on 28/Feb/15 $${a}=\mathrm{0} \\ $$$$\frac{{b}}{{bx}−\mathrm{1}}={b},{b}=\mathrm{0},\forall{x}\neq\frac{\mathrm{1}}{{b}} \\…
Question Number 669 by 112358 last updated on 21/Feb/15 $${Given}\:{only}\:{the}\:{standard}\:{result}\:\underset{{r}=\mathrm{1}} {\overset{{N}} {\sum}}{r}^{\mathrm{2}} =\frac{\mathrm{1}}{\mathrm{6}}{N}\left({N}+\mathrm{1}\right)\left(\mathrm{2}{N}+\mathrm{1}\right)\: \\ $$$${is}\:{applied}\:{to}\:{determining}\:{the}\:{series} \\ $$$$\mathrm{1}^{\mathrm{2}} +\mathrm{2}×\mathrm{2}^{\mathrm{2}} +\mathrm{3}^{\mathrm{2}} +\mathrm{2}×\mathrm{4}^{\mathrm{2}} +\mathrm{5}^{\mathrm{2}} +\mathrm{2}×\mathrm{6}^{\mathrm{2}} +\mathrm{7}^{\mathrm{2}} +…+\mathrm{2}\left({n}−\mathrm{1}\right)^{\mathrm{2}} +{n}^{\mathrm{2}}…
Question Number 66199 by aliesam last updated on 10/Aug/19 $${calculate} \\ $$$${cos}\left(\mathrm{79}\right)=? \\ $$ Commented by $@ty@m123 last updated on 10/Aug/19 $${Use}\:{trigonometrical}\:{table}. \\ $$$${OR}\: \\…
Question Number 66197 by Rasheed.Sindhi last updated on 11/Aug/19 $$\mathrm{If}\:\:\mathrm{x}+\frac{\mathrm{1}}{\mathrm{x}}=\mathrm{1},\mathrm{prove}\:\mathrm{that}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{x}^{\mathrm{n}} +\mathrm{x}^{\mathrm{n}−\mathrm{2}} +\mathrm{x}^{\mathrm{n}−\mathrm{4}} =\mathrm{0} \\ $$ Commented by mr W last updated on 10/Aug/19…
Question Number 647 by 123456 last updated on 18/Feb/15 $$\mathrm{log}_{{x}} \left({y}^{\pi} \right)+\mathrm{log}_{{y}} \left({x}^{{e}} \right)={a} \\ $$$$\frac{\mathrm{1}}{\mathrm{log}_{{y}} \left({x}^{\pi^{−\mathrm{1}} } \right)}−\frac{\mathrm{1}}{\mathrm{log}_{{x}} \left({y}^{{e}^{−\mathrm{1}} } \right)}={b} \\ $$$$\frac{{x}^{{a}+{b}+\mathrm{2}{e}} }{{y}^{{a}−{b}+\mathrm{2}\pi}…
Question Number 131697 by mathlove last updated on 07/Feb/21 $${x}^{{x}} =\mathrm{6}\:\:\:\:\:\:\:\:\:\:{x}=? \\ $$ Answered by mr W last updated on 07/Feb/21 $${x}=\mathrm{6}^{\frac{\mathrm{1}}{{x}}} ={e}^{\frac{\mathrm{ln}\:\mathrm{6}}{{x}}} \\ $$$$\frac{\mathrm{1}}{{x}}{e}^{\frac{\mathrm{ln}\:\mathrm{6}}{{x}}}…
Question Number 619 by Cheenz last updated on 11/Feb/15 $$\sqrt{\mathrm{2}+\sqrt{\mathrm{3}}}\:+\:\sqrt{\mathrm{2}−\sqrt{\mathrm{3}}}\:=\:? \\ $$ Answered by 123456 last updated on 11/Feb/15 $${x}=\sqrt{\mathrm{2}+\sqrt{\mathrm{3}}}+\sqrt{\mathrm{2}−\sqrt{\mathrm{3}}} \\ $$$${x}^{\mathrm{2}} =\mathrm{2}+\sqrt{\mathrm{3}}+\mathrm{2}\sqrt{\mathrm{2}+\sqrt{\mathrm{3}}}\sqrt{\mathrm{2}−\sqrt{\mathrm{3}}}+\mathrm{2}−\sqrt{\mathrm{3}} \\ $$$${x}^{\mathrm{2}}…
Question Number 131688 by liberty last updated on 07/Feb/21 $$\:\mathrm{Let}\:\alpha\:\mathrm{and}\:\beta\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\: \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{x}^{\mathrm{2}} −\mathrm{6x}−\mathrm{2}=\mathrm{0}. \\ $$$$\mathrm{If}\:{a}_{{n}} \:=\:\alpha^{{n}} −\beta^{{n}} \:\mathrm{for}\:{n}\:\geqslant\mathrm{1}\: \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\frac{{a}_{\mathrm{10}} −\mathrm{2}{a}_{\mathrm{8}} }{\mathrm{2}{a}_{\mathrm{9}} }\:? \\ $$…
Question Number 66126 by Joel122 last updated on 09/Aug/19 $$\mathrm{Is}\:\mathrm{there}\:\mathrm{any}\:\mathrm{formula}\:\mathrm{to}\:\mathrm{find}\:\mathrm{sum}\:\mathrm{of} \\ $$$$\mathrm{1}\:+\:{n}^{\mathrm{2}} \:+\:{n}^{\mathrm{4}} \:+\:{n}^{\mathrm{6}} \:+\:{n}^{\mathrm{8}} \:+\:…\:+\:{n}^{\mathrm{2}{k}} \:+\:… \\ $$$$\mathrm{where}\:{n},{k}\:\in\:\mathbb{Z}^{+} \: \\ $$ Answered by mr…