Question Number 41820 by v tfvhjdxf last updated on 13/Aug/18 $$\mathrm{If}\:\alpha,\:\beta\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$${ax}^{\mathrm{2}} +{bx}+{c}=\mathrm{0},\:\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{determinant} \\ $$$$\begin{vmatrix}{\mathrm{1}}&{\mathrm{cos}\:\left(\beta−\alpha\right)}&{\mathrm{cos}\:\alpha}\\{\mathrm{cos}\:\left(\alpha−\beta\right)}&{\mathrm{1}}&{\mathrm{cos}\:\beta}\\{\mathrm{cos}\:\alpha}&{\mathrm{cos}\:\beta}&{\mathrm{1}}\end{vmatrix}\:\mathrm{is} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated…
Question Number 107330 by saorey0202 last updated on 10/Aug/20 $$\mathrm{If}\:\:\:{a}+{b}+{c}=\mathrm{0}\:\mathrm{one}\:\mathrm{root}\:\mathrm{of} \\ $$$$\begin{vmatrix}{{a}−{x}}&{\:\:\:\:{c}}&{\:\:\:{b}}\\{\:\:\:\:{c}}&{{b}−{x}}&{\:\:\:{a}}\\{\:\:\:\:{b}}&{\:\:\:{a}}&{{c}−{x}}\end{vmatrix}=\mathrm{0}\:\mathrm{is} \\ $$ Answered by som(math1967) last updated on 10/Aug/20 $$\begin{vmatrix}{\mathrm{a}+\mathrm{b}+\mathrm{c}−\mathrm{x}}&{\mathrm{a}+\mathrm{b}+\mathrm{c}−\mathrm{x}}&{\mathrm{a}+\mathrm{b}+\mathrm{c}−\mathrm{x}}\\{\mathrm{c}}&{\mathrm{b}−\mathrm{x}}&{\mathrm{a}}\\{\mathrm{b}}&{\mathrm{a}}&{\mathrm{c}−\mathrm{x}}\end{vmatrix}=\mathrm{0} \\ $$$$\left[\mathrm{R}_{\mathrm{1}} ^{'}…
Question Number 107331 by saorey0202 last updated on 10/Aug/20 $$\mathrm{If}\:{A}\:\mathrm{is}\:\mathrm{an}\:\mathrm{invertible}\:\mathrm{matrix},\:\mathrm{then}\:\mathrm{det}\left({A}^{−\mathrm{1}} \right) \\ $$$$\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$ Answered by udaythool last updated on 10/Aug/20 $${AA}^{−\mathrm{1}} ={I} \\…
Question Number 41579 by Dawajan Nikmal last updated on 09/Aug/18 $$\mathrm{If}\:\:{u}_{\mathrm{10}} =\:\underset{\:\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}{x}^{\mathrm{10}} \:\mathrm{sin}\:{x}\:{dx},\:\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$${u}_{\mathrm{10}} +\mathrm{90}\:{u}_{\mathrm{8}} \:\:\mathrm{is} \\ $$ Commented by maxmathsup by…
Question Number 41578 by Dawajan Nikmal last updated on 09/Aug/18 $$\mathrm{If}\:\:{u}_{\mathrm{10}} =\:\underset{\:\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}{x}^{\mathrm{10}} \:\mathrm{sin}\:{x}\:{dx},\:\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$${u}_{\mathrm{10}} +\mathrm{90}\:{u}_{\mathrm{8}} \:\:\mathrm{is} \\ $$ Terms of Service Privacy…
Question Number 41577 by Dawajan Nikmal last updated on 09/Aug/18 $$\mathrm{If}\:\:{u}_{\mathrm{10}} =\:\underset{\:\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}{x}^{\mathrm{10}} \:\mathrm{sin}\:{x}\:{dx},\:\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$${u}_{\mathrm{10}} +\mathrm{90}\:{u}_{\mathrm{8}} \:\:\mathrm{is} \\ $$ Terms of Service Privacy…
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Question Number 41495 by Dawajan Nikmal last updated on 08/Aug/18 $$\mathrm{The}\:\mathrm{equation}\:\pi^{{x}} =−\mathrm{2}{x}^{\mathrm{2}} +\mathrm{6}{x}−\mathrm{9}\:\mathrm{has} \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on 09/Aug/18 $${no}\:{solution} \\ $$…
Question Number 41291 by Mayur last updated on 04/Aug/18 $$\mathrm{Let}\:{ABCD}\:\mathrm{be}\:\mathrm{a}\:\mathrm{parallelogram}\:\mathrm{whose} \\ $$$$\mathrm{diagonals}\:\mathrm{intersect}\:\mathrm{at}\:{P}\:\mathrm{and}\:\mathrm{ley}\:{O}\:\mathrm{be} \\ $$$$\mathrm{the}\:\mathrm{origin},\:\mathrm{then}\:\overset{\rightarrow} {{OA}}+\overset{\rightarrow} {{OB}}+\overset{\rightarrow} {{OC}}+\overset{\rightarrow} {{OD}}\: \\ $$$$\mathrm{equals} \\ $$ Answered by MJS…
Question Number 41141 by Kishan Daroga last updated on 02/Aug/18 $$\mathrm{If}\:{X}=\begin{bmatrix}{\mathrm{3}}&{−\mathrm{4}}\\{\mathrm{1}}&{−\mathrm{1}}\end{bmatrix},\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{X}^{{n}} \mathrm{is} \\ $$ Commented by math khazana by abdo last updated on 04/Aug/18 $${let}\:{A}\:=\:\begin{pmatrix}{\mathrm{3}\:\:\:\:\:\:\:−\mathrm{4}}\\{\mathrm{1}\:\:\:\:\:\:\:\:\:−\mathrm{1}}\end{pmatrix}\:\:{the}\:{caracteristic}\:{polynome}\:{of}…