Question Number 10793 by j.masanja06@gmail.com last updated on 25/Feb/17 $$\mathrm{let}\:\:\mathrm{A}\:=\begin{vmatrix}{\mathrm{4}}&{\mathrm{4k}}&{\mathrm{k}}\\{\mathrm{0}}&{\mathrm{k}}&{\mathrm{4k}}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{4}}\end{vmatrix}\:\mathrm{if}\:\mathrm{det}\left(\mathrm{A}^{\mathrm{2}} \right)=\mathrm{16} \\ $$$$\mathrm{then}\:\mid\mathrm{k}\mid\:\mathrm{is}? \\ $$ Answered by sandy_suhendra last updated on 25/Feb/17 $$\mathrm{det}\:\mathrm{A}=\mathrm{16k}+\mathrm{0}+\mathrm{0}−\left(\mathrm{0}+\mathrm{0}+\mathrm{0}\right)=\mathrm{16k} \\ $$$$\mathrm{det}\left(\mathrm{A}^{\mathrm{2}}…
Question Number 10789 by niraj last updated on 25/Feb/17 $$\left(\mathrm{2}+\mathrm{3}{i}\right){x}^{\mathrm{2}} −\left(\mathrm{3}−\mathrm{2}{i}\right){y}=\mathrm{2}{x}−\mathrm{3}{y}+\mathrm{5}{i} \\ $$ Answered by sandy_suhendra last updated on 25/Feb/17 $$\left(\mathrm{2}+\mathrm{3i}\right)\mathrm{x}^{\mathrm{2}} −\mathrm{3y}+\mathrm{2iy}=\mathrm{2x}−\mathrm{3y}+\mathrm{5i} \\ $$$$\Rightarrow\:\left(\mathrm{2}+\mathrm{3i}\right)\mathrm{x}^{\mathrm{2}} =\mathrm{2x}…
Question Number 10774 by j.masanja06@gmail.com last updated on 24/Feb/17 Answered by sandy_suhendra last updated on 24/Feb/17 $$=\begin{vmatrix}{\mathrm{log}_{\mathrm{3}} \mathrm{1024}\:\:\:\:\mathrm{1}}\\{\mathrm{log}_{\mathrm{3}} \mathrm{8}\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}}\end{vmatrix}×\begin{vmatrix}{\mathrm{log}_{\mathrm{2}} \mathrm{3}\:\:\:\:\mathrm{log}_{\mathrm{4}} \mathrm{3}}\\{\mathrm{log}_{\mathrm{3}} \mathrm{4}\:\:\:\:\mathrm{log}_{\mathrm{3}} \mathrm{4}}\end{vmatrix} \\ $$$$=\left(\mathrm{2log}_{\mathrm{3}}…
Question Number 10776 by j.masanja06@gmail.com last updated on 24/Feb/17 $$\mathrm{if}\:\:\:\mathrm{D}\:=\begin{vmatrix}{\mathrm{1}}&{\mathrm{3sin}\theta}&{\mathrm{1}}\\{\mathrm{sin}\theta}&{\mathrm{1}}&{\mathrm{3cos}\theta}\\{\mathrm{1}}&{\mathrm{sin}\theta}&{\mathrm{1}}\end{vmatrix}\:\mathrm{the}\:\mathrm{maxi} \\ $$$$\mathrm{mum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{D}\:\mathrm{is}? \\ $$ Answered by sandy_suhendra last updated on 24/Feb/17 $$\mathrm{D}=\mathrm{1}+\mathrm{9}\:\mathrm{sin}\theta\:\mathrm{cos}\theta+\mathrm{sin}\theta\:\mathrm{cos}\theta−\left(\mathrm{1}+\mathrm{3}\:\mathrm{sin}\theta\:\mathrm{cos}\theta+\mathrm{3}\:\mathrm{sin}\theta\:\mathrm{cos}\theta\right)\:\:\:\:\: \\ $$$$\:\:\:\:=\mathrm{4}\:\mathrm{sin}\theta\:\mathrm{cos}\theta=\mathrm{2}\:\mathrm{sin}\:\mathrm{2}\theta \\…
Question Number 10777 by j.masanja06@gmail.com last updated on 24/Feb/17 $$\:\mathrm{find}\:\mathrm{the}\:\mathrm{range}\:\mathrm{or}\:\left(\mathrm{ranges}\right)\:\mathrm{of}\:\mathrm{value}\:\mathrm{x} \\ $$$$\mathrm{can}\:\mathrm{take}\:\mathrm{for}\:\:\mathrm{x}+\mathrm{6}>\left[\mathrm{2x}+\mathrm{3}\right] \\ $$ Commented by mrW1 last updated on 24/Feb/17 $${do}\:{you}\:{mean}\:{x}+\mathrm{6}>\mid\mathrm{2}{x}+\mathrm{3}\mid\:? \\ $$ Commented…
Question Number 141846 by ArielVyny last updated on 24/May/21 $$\sum_{{k}\geqslant\mathrm{0}} \left({C}_{{n}} ^{{k}} \right)^{\mathrm{2}} \\ $$ Answered by mindispower last updated on 24/May/21 $$\underset{{k}\geqslant\mathrm{0}} {\sum}{C}_{{n}} ^{{k}}…
Question Number 76307 by Master last updated on 26/Dec/19 Answered by mr W last updated on 26/Dec/19 $${x}\neq\mathrm{1} \\ $$$$\mathrm{125}\left(\mathrm{1}+{x}^{\mathrm{5}} \right)=\mathrm{11}\left(\mathrm{1}+{x}\right)^{\mathrm{5}} \\ $$$$\mathrm{125}\left(\mathrm{1}−{x}+{x}^{\mathrm{2}} −{x}^{\mathrm{3}} +{x}^{\mathrm{4}}…
Question Number 10755 by Joel576 last updated on 24/Feb/17 $${x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:+\:{xy}\:+\:\mathrm{2}\left({x}\:−\:{y}\right)\:=\:\mathrm{9} \\ $$$$\mathrm{How}\:\mathrm{many}\:\mathrm{solution}\:\mathrm{that}\:\mathrm{fulfilled}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{above}\:? \\ $$$${x},\:{y}\:\in\:\mathbb{N} \\ $$ Answered by mrW1 last updated on 24/Feb/17…
Question Number 76290 by benjo last updated on 26/Dec/19 $$\mathrm{how}\:\mathrm{to}\:\mathrm{prove}\:\mathrm{x}^{\mathrm{y}} \:+\mathrm{y}^{\mathrm{x}} \:\geqslant\mathrm{1}\:,\:\mathrm{x},\mathrm{y}\:\in\mathbb{R} \\ $$$$\mathrm{x},\mathrm{y}\:>\:\mathrm{0} \\ $$ Commented by MJS last updated on 26/Dec/19 $$\mathrm{we}\:\mathrm{can}\:\mathrm{exchange}\:{x}\:\mathrm{and}\:{y}\:\Rightarrow\:\mathrm{let}\:{x}\leqslant{y} \\…
Question Number 141822 by mathsuji last updated on 23/May/21 Commented by MJS_new last updated on 23/May/21 $$\mathrm{where}\:\mathrm{you}\:\mathrm{found}\:\mathrm{this}? \\ $$$$\mathrm{did}\:\mathrm{your}\:\mathrm{teacher}\:\mathrm{gave}\:\mathrm{it}\:\mathrm{to}\:\mathrm{you}?\:\mathrm{which}\:\mathrm{chapter} \\ $$$$\mathrm{of}\:\mathrm{solving}\:\mathrm{equations}\:\mathrm{are}\:\mathrm{you}\:\mathrm{studying}? \\ $$$$\mathrm{have}\:\mathrm{you}\:\mathrm{got}\:\mathrm{any}\:\mathrm{idea}? \\ $$$$\bullet\:\mathrm{yes}:\:\mathrm{then}\:\mathrm{please}\:\mathrm{tell}\:\mathrm{us}…