Category: Algebra

Question Number 205746 by Satyam1234 last updated on 29/Mar/24 Answered by A5T last updated on 29/Mar/24 $$C\ne J+2\Rightarrow C=3F$$$$A⩾1;A=1\Rightarrow B=3\Rightarrow I=7\Rightarrow H=4\Rightarrow A=8X$$$$A=2\Rightarrow B=6\Rightarrow E=2X$$$$A=3\Rightarrow B=9X(6\Rightarrow B<5orA⩾4)orG=0$$$$\:\left({G}=\mathrm{0}\Rightarrow{I}=\mathrm{3}\Rightarrow{D}=\mathrm{6}\Rightarrow{E}=\mathrm{18}\right){X}…

Question Number 205733 by hardmath last updated on 28/Mar/24 $$\mathrm{If}\mathrm{a},\mathrm{b},\mathrm{c}\in {\mathbb{R}}^{+}\mathrm{and}\mathrm{a}+\mathrm{b}+\mathrm{c}=6$$$$\mathrm{Prove}\mathrm{that}:$$$$\frac{{\mathrm{a}}^2-4}{{4\mathrm{a}}^2-9\mathrm{a}+6}+\frac{{\mathrm{b}}^2-4}{{4\mathrm{b}}^2-9\mathrm{b}+6}+\frac{{\mathrm{c}}^2-4}{{4\mathrm{c}}^2-9\mathrm{c}+6}⩽0$$ Answered by…

Question Number 205645 by hardmath last updated on 26/Mar/24 $$\mathrm{Find}:\mathrm{\Omega }={\int }_0^{\frac{\mathit{\pi }}{2}}\frac{{\sin }^2\mathrm{x}}{2\mathrm{cosx}+3\mathrm{sinx}}\mathrm{dx}=?$$ Answered by Frix last updated on 26/Mar/24 $$t=\tan \frac{x}{2}\mathrm{leads}\mathrm{to}$$$$−\mathrm{4}\int\frac{{t}^{\mathrm{2}}…

Question Number 205643 by hardmath last updated on 26/Mar/24 $$\mathrm{If}\mathrm{a},\mathrm{b},\mathrm{c}>0\mathrm{and}{\mathrm{a}}^2+{\mathrm{b}}^2+{\mathrm{c}}^2=\mathrm{abc}$$$$\mathrm{Prove}\mathrm{that}:$$$$\frac{\mathrm{a}}{{\mathrm{a}}^2+\mathrm{bc}}+\frac{\mathrm{b}}{{\mathrm{b}}^2+\mathrm{ac}}+\frac{\mathrm{c}}{{\mathrm{c}}^2+\mathrm{ab}}⩽\frac{1}{2}$$ Answered by A5T…

Question Number 205669 by hardmath last updated on 26/Mar/24 Answered by Berbere last updated on 27/Mar/24 $$A=X^5$$$${\chi }_A=(3-x)(5-x)-8=X^2-8X+7$$$$(x-1)(X-7)D=\left(\begin{array}{c}10\\ 07\end{array}\right)$$$${U}_{\mathrm{1}}…