Question Number 96437 by bemath last updated on 01/Jun/20 Answered by bobhans last updated on 01/Jun/20 $$\boldsymbol{{xy}}−\mathrm{3}\boldsymbol{{x}}+\mathrm{5}\boldsymbol{{y}}−\mathrm{15}\:=\:−\mathrm{15} \\ $$$$\left(\boldsymbol{{x}}+\mathrm{5}\right)\left(\boldsymbol{{y}}−\mathrm{3}\right)\:=\:−\mathrm{15} \\ $$$$\left(\mathrm{1}\right)\:\boldsymbol{{x}}+\mathrm{5}\:=\:\pm\mathrm{1};\:\mathrm{y}−\mathrm{3}\:=\:\mp\mathrm{15} \\ $$$$\left(\mathrm{2}\right){x}+\mathrm{5}\:=\:\pm\:\mathrm{3}\:;\:\mathrm{y}−\mathrm{3}\:=\:\mp\:\mathrm{5}\: \\ $$$$\left(\mathrm{3}\right)\:{x}+\mathrm{5}\:=\:\pm\mathrm{5}\:;\:\mathrm{y}−\mathrm{3}\:=\:\mp\:\mathrm{3}…
Question Number 30897 by usman katyar last updated on 28/Feb/18 $$\left(\mathrm{44}{x}+\mathrm{28}{y}\right)\mathrm{2} \\ $$ Commented by rahul 19 last updated on 28/Feb/18 $$? \\ $$$$\mathrm{88}{x}+\mathrm{56}{y}\:. \\…
Question Number 161860 by Rasheed.Sindhi last updated on 23/Dec/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{Simplify} \\ $$$$\frac{\mathrm{1}^{\mathrm{2}} \centerdot\mathrm{2}!+\mathrm{2}^{\mathrm{2}} \centerdot\mathrm{3}!+\mathrm{3}^{\mathrm{2}} \centerdot\mathrm{4}!+\centerdot\centerdot\centerdot+{n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)!−\mathrm{2}}{\left({n}+\mathrm{1}\right)!} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{to} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{n}^{\mathrm{2}} +\mathrm{n}−\mathrm{2} \\ $$ Answered by…
Question Number 161843 by Rasheed.Sindhi last updated on 23/Dec/21 $${Q}#\mathrm{161744}\:{reposted}\:{with}\:{some}\:{change}. \\ $$$$\mathrm{Solve}\:\mathrm{for}\:\boldsymbol{\mathrm{integer}}\:\mathrm{numbers}: \\ $$$$\frac{\mathrm{x}}{\mathrm{y}}\:+\:\frac{\mathrm{5}}{\mathrm{x}}\:+\:\frac{\mathrm{y}\:-\:\mathrm{5}}{\mathrm{5}}\:=\:\frac{\mathrm{y}\:+\:\mathrm{x}}{\mathrm{y}\:+\:\mathrm{5}}\:+\:\frac{\mathrm{5}\:+\:\mathrm{y}}{\mathrm{5}\:+\:\mathrm{x}} \\ $$ Commented by malwan last updated on 23/Dec/21 $${x}=\mathrm{0}\:{or}\:{x}=\mathrm{5} \\…
Question Number 30687 by Rasheed.Sindhi last updated on 24/Feb/18 $$\mathrm{Given}\:\mathrm{that}\:\mathrm{LCM}\left(\mathrm{A},\mathrm{B},\mathrm{C}\right)=\mathrm{252} \\ $$$$\mathrm{LCM}\left(\mathrm{A},\mathrm{B}\right)=\mathrm{36}\:\&\:\mathrm{LCM}\left(\mathrm{A},\mathrm{C}\right)=\mathrm{63}; \\ $$$$\mathrm{then}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{LCM}\left(\mathrm{B},\mathrm{C}\right)=? \\ $$$$\mathrm{Pl}\:\mathrm{determine}\:\mathrm{all}\:\mathrm{possible}\:\mathrm{answers}. \\ $$ Answered by MJS last updated…
Question Number 161622 by amin96 last updated on 20/Dec/21 $$\underset{\boldsymbol{{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{\boldsymbol{{n}}+\mathrm{1}} }{\boldsymbol{{n}}\left(\mathrm{2}\boldsymbol{{n}}+\mathrm{1}\right)}=? \\ $$ Answered by mathmax by abdo last updated on 20/Dec/21 $$\frac{\mathrm{S}}{\mathrm{2}}=−\sum_{\mathrm{n}=\mathrm{1}}…
Question Number 161528 by Rasheed.Sindhi last updated on 19/Dec/21 $$\mathrm{PROVE}\:\mathrm{that}\:\mathrm{the}\:\mathrm{numbers}\:\mathrm{of}\:\mathrm{types} \\ $$$$\mathrm{4k}+\mathrm{2}\:\&\:\mathrm{4k}+\mathrm{3}\:\mathrm{are}\:\mathrm{NOT}\:\mathrm{perfect}\:\Box\mathrm{s}. \\ $$ Answered by mr W last updated on 19/Dec/21 $$\left(\mathrm{1}\right)\:{type}\:\mathrm{4}{k}+\mathrm{3} \\ $$$${assume}\:{it}\:{can}\:{be}\:{a}\:{perfect}\:{square}.…
Question Number 95966 by i jagooll last updated on 29/May/20 $$\mathrm{find}\:\mathrm{all}\:\mathrm{pairs}\:\mathrm{of}\:\mathrm{integer}\:\mathrm{for}\: \\ $$$$\mathrm{xy}+\mathrm{3x}−\mathrm{4y}\:=\:\mathrm{29}\: \\ $$ Answered by john santu last updated on 29/May/20 $$\Rightarrow\mathrm{3}{x}+{xy}−\mathrm{4}{y}−\mathrm{12}\:=\:\mathrm{17}\: \\…
Question Number 95897 by john santu last updated on 28/May/20 $$\mathrm{If}\:{x}\in\mathbb{C}\:.\:\mathrm{find}\:\mathrm{solution}\:\mathrm{of}\: \\ $$$$\mathrm{3}+{i}\sqrt{\mathrm{2}}\:=\:{e}^{{ix}} \: \\ $$ Answered by bobhans last updated on 28/May/20 $$\mathrm{3}+{i}\sqrt{\mathrm{2}}\:=\:{e}^{{ix}} \:…
Question Number 95868 by rb222 last updated on 28/May/20 $$\mathrm{5}^{\mathrm{10}} \left({mod}\:\mathrm{11}\right)=? \\ $$ Commented by Rasheed.Sindhi last updated on 28/May/20 $$\mathrm{5}^{\mathrm{5}} \equiv\mathrm{1}\left({mod}\:\mathrm{11}\right) \\ $$$$\left(\mathrm{5}^{\mathrm{5}} \right)^{\mathrm{2}}…