Category: Algebra

Question Number 158364 by HongKing last updated on 03/Nov/21 $$\mathrm{if}\mathrm{a};\mathrm{b};\mathrm{c}>0\mathrm{prove}\mathrm{that}:$$$${\mathrm{a}}^{2\mathbf{a}-(\mathbf{b}+\mathbf{c})}\cdot {\mathrm{b}}^{2\mathbf{b}-(\mathbf{c}+\mathbf{a})}\cdot {\mathrm{c}}^{2\mathbf{c}-(\mathbf{a}+\mathbf{b})}⩾1$$$$$$ Terms of Service Privacy Policy Contact:…

Question Number 92831 by unknown last updated on 09/May/20 Commented by unknown last updated on 09/May/20 $$\mathrm{Solve}\mathrm{the}\mathrm{equation}(p,q,r)\mathrm{if}\mathrm{the}\mathrm{solution}\mathrm{are}\mathrm{real}\mathrm{number}$$ Commented by unknown last updated on…

Question Number 158366 by HongKing last updated on 03/Nov/21 Answered by MathsFan last updated on 03/Nov/21 $$\frac{\mathrm{lne}}{\mathrm{lnx}\bullet \mathrm{lnx}}+\frac{\mathrm{lne}}{(\mathrm{lne}-\mathrm{lnx})(\mathrm{lne}-\mathrm{lnx})}=8$$$$\mathrm{say}\mathrm{a}=\mathrm{lnx}$$$$\frac{1}{{\mathrm{a}}^2}+\frac{1}{1-2\mathrm{a}+{\mathrm{a}}^2}=8$$$$\:\mathrm{2a}^{\mathrm{2}}…

Question Number 158331 by HongKing last updated on 02/Nov/21 $$\mathrm{Prove}\mathrm{that}:$$$$\underset{\mathbf{n}=1}{\sum ^{\mathrm{\infty }}}\frac{1}{\sqrt{\mathrm{n}}(\mathrm{n}+1)}<2$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 158313 by mnjuly1970 last updated on 02/Nov/21 Answered by mr W last updated on 02/Nov/21 $$\alpha ,\beta ,\gamma areanglesofatriangle.$$$$F=\frac{\sin \alpha \cos \alpha +\sin \beta \cos \beta +\sin \gamma \cos \gamma }{\sin \alpha \sin \beta \sin \gamma }$$$$F=\frac{\sin 2\alpha +\sin 2\beta +\sin 2\gamma }{2\sin \alpha \sin \beta \sin \gamma }$$$${F}=\frac{\mathrm{4}\:\mathrm{sin}\:\alpha\:\mathrm{sin}\:\beta\:\mathrm{sin}\:\gamma}{\mathrm{2}\:\mathrm{sin}\:\alpha\:\mathrm{sin}\:\beta\:\mathrm{sin}\:\gamma} \…