Question Number 80144 by behi83417@gmail.com last updated on 31/Jan/20 $$\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{x}}: \\ $$$$\frac{\sqrt{\boldsymbol{\mathrm{x}}}+\mathrm{1}}{\:\sqrt{\boldsymbol{\mathrm{x}}+\mathrm{1}}}+\boldsymbol{\mathrm{ax}}^{\mathrm{2}} =\boldsymbol{\mathrm{x}}\left(\boldsymbol{\mathrm{a}}^{\mathrm{2}} +\mathrm{1}\right)\:\:\:\:\:\:\left[\boldsymbol{\mathrm{a}}\in\boldsymbol{\mathrm{R}}\right] \\ $$ Commented by john santu last updated on 31/Jan/20 $${let}\:\sqrt{{x}+\mathrm{1}}\:=\:\mathrm{sec}\:{t}…
Question Number 145683 by imjagoll last updated on 07/Jul/21 $$\:\frac{\mathrm{3}\:\sqrt[{\sqrt{\mathrm{4}}}]{\mathrm{360}}\:−\mathrm{2}\:\sqrt[{!\mathrm{3}}]{\mathrm{162}}}{\:\sqrt{\mathrm{10}}−\sqrt{\mathrm{2}}}\:=? \\ $$ Answered by puissant last updated on 07/Jul/21 $$\sqrt{\mathrm{4}}=\mathrm{2}\:\:;\:\:!\mathrm{3}=\:\:\mathrm{3}!\mid\frac{\mathrm{1}!}{\mathrm{0}!}−\frac{\mathrm{1}!}{\mathrm{1}!}−\frac{\mathrm{1}!}{\mathrm{2}!}+\frac{\mathrm{1}!}{\mathrm{3}!}\mid \\ $$$$\Rightarrow\frac{\mathrm{3}\sqrt{\mathrm{360}}−\mathrm{2}\sqrt{\mathrm{162}}}{\:\sqrt{\mathrm{10}}−\sqrt{\mathrm{2}}}=\frac{\mathrm{18}\sqrt{\mathrm{10}}−\mathrm{18}\sqrt{\mathrm{2}}}{\:\sqrt{\mathrm{10}}−\sqrt{\mathrm{2}}} \\ $$$$=\frac{\mathrm{18}\left(\sqrt{\mathrm{10}}−\sqrt{\mathrm{2}}\right)}{\left(\sqrt{\mathrm{10}}−\sqrt{\mathrm{2}}\right)}\:=\:\mathrm{18}.. \\…
Question Number 80142 by behi83417@gmail.com last updated on 31/Jan/20 $$\mathrm{a}.\:\:\:\underset{\boldsymbol{\mathrm{k}}=\mathrm{1}} {\overset{\infty} {\sum}}\:\:\left(\frac{\boldsymbol{\mathrm{k}}^{\mathrm{3}} }{\mathrm{2}^{\boldsymbol{\mathrm{k}}} }\right)=? \\ $$$$\boldsymbol{\mathrm{b}}.\:\:\:\:\underset{\boldsymbol{\mathrm{k}}=\mathrm{1}} {\overset{\infty} {\sum}}\:\:\left(\frac{\boldsymbol{\mathrm{k}}^{\mathrm{3}} +\boldsymbol{\mathrm{k}}^{\mathrm{2}} +\boldsymbol{\mathrm{k}}+\mathrm{1}}{\mathrm{7}^{\boldsymbol{\mathrm{k}}} }\right)=? \\ $$ Answered by…
Question Number 80145 by behi83417@gmail.com last updated on 31/Jan/20 $$\begin{cases}{\frac{\boldsymbol{\mathrm{x}}}{\boldsymbol{\mathrm{a}}}+\frac{\boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{b}}}=\boldsymbol{\mathrm{a}}^{\mathrm{2}} +\boldsymbol{\mathrm{b}}^{\mathrm{2}} }\\{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left[\boldsymbol{\mathrm{a}},\boldsymbol{\mathrm{b}}\in\boldsymbol{\mathrm{R}}\right]}\\{\boldsymbol{\mathrm{ab}}\left(\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\boldsymbol{\mathrm{y}}^{\mathrm{2}} \right)=\boldsymbol{\mathrm{xy}}\left(\boldsymbol{\mathrm{a}}^{\mathrm{2}} −\boldsymbol{\mathrm{b}}^{\mathrm{2}} \right)}\end{cases} \\ $$ Commented by john santu last updated on…
Question Number 80139 by M±th+et£s last updated on 31/Jan/20 Commented by M±th+et£s last updated on 31/Jan/20 $$\left[{Q}\mathrm{80131}\:{Reposted}\right] \\ $$ Commented by mr W last updated…
Question Number 145668 by mathdanisur last updated on 07/Jul/21 $${Compare}: \\ $$$${sin}\left(\mathrm{43}°\right)\:\:{and}\:\:{sin}\left(\mathrm{40}°\right)+{sin}\left(\mathrm{3}°\right) \\ $$ Answered by mr W last updated on 07/Jul/21 $$\mathrm{sin}\:\mathrm{43}°=\mathrm{sin}\:\left(\mathrm{40}+\mathrm{3}\right) \\ $$$$=\mathrm{cos}\:\mathrm{3}×\mathrm{sin}\:\mathrm{40}+\mathrm{cos}\:\mathrm{40}×\mathrm{sin}\:\mathrm{3}…
Question Number 145664 by qaz last updated on 07/Jul/21 $$\mathrm{S}=\underset{\mathrm{k}=\mathrm{0}} {\overset{\mathrm{n}} {\sum}}\left(−\mathrm{1}\right)^{\mathrm{k}} \mathrm{k}^{\mathrm{3}} =? \\ $$ Answered by mathmax by abdo last updated on 07/Jul/21…
Question Number 14594 by 1kanika# last updated on 02/Jun/17 Answered by Tinkutara last updated on 02/Jun/17 $${f}\left({x}\right)\:=\:{Q}\left({x}\:−\:\mathrm{2}\right)\left({x}\:−\:\mathrm{3}\right)\:+\:{ax}\:+\:{b} \\ $$$$\mathrm{3}{a}\:+\:{b}\:=\:\mathrm{2} \\ $$$$\mathrm{2}{a}\:+\:{b}\:=\:\mathrm{3} \\ $$$$\Rightarrow\:{a}\:=\:−\mathrm{1},\:{b}\:=\:\mathrm{5} \\ $$$$\mathrm{Remainder}\:\mathrm{when}\:\mathrm{divided}\:\mathrm{by}…
Question Number 80131 by M±th+et£s last updated on 31/Jan/20 Commented by MJS last updated on 31/Jan/20 $$+\infty \\ $$$$\mathrm{e}^{\frac{\pi}{\mathrm{2}}} \approx\mathrm{4}.\mathrm{8} \\ $$$$\mathrm{4}.\mathrm{8}^{\mathrm{4}.\mathrm{8}} \approx\mathrm{1913} \\ $$$$……
Question Number 145666 by mathdanisur last updated on 07/Jul/21 Answered by Rasheed.Sindhi last updated on 07/Jul/21 $$\mid{x}+\mathrm{1}\mid+\sqrt{{x}^{\mathrm{2}} −\mathrm{4}{x}−\mathrm{4}}+\mid{x}−{z}\mid+\mid{z}−\mathrm{3}\mid=\mathrm{4} \\ $$$$….. \\ $$$$…. \\ $$ Commented…