Category: Algebra

Question Number 151371 by mathdanisur last updated on 20/Aug/21 $$\mathrm{a};\mathrm{b}\in \mathbb{N}$$$${(\mathrm{a}+\mathrm{b})}^2\cdot (\mathrm{a}-\mathrm{b})=128$$$$\mathrm{ab}=?$$ Answered by nimnim last updated on 20/Aug/21 $$\mathrm{a};\mathrm{b}\in\mathrm{N}…

Question Number 20296 by Tinkutara last updated on 25/Aug/17 $$\mathrm{If}(m_r,\frac{1}{m_r});r=1,2,3,4\mathrm{be}\mathrm{four}\mathrm{pairs}$$$$\mathrm{of}\mathrm{values}\mathrm{of}x\mathrm{and}y\mathrm{satisfy}\mathrm{the}\mathrm{equation}$$$$x^2+y^2+2gx+2fy+c=0,\mathrm{then}\mathrm{prove}$$$$\mathrm{that}\:{m}_{\mathrm{1}} .{m}_{\mathrm{2}} .{m}_{\mathrm{3}} .{m}_{\mathrm{4}} \:=\:\mathrm{1}. \…

Question Number 151361 by mathdanisur last updated on 20/Aug/21 $$\mathrm{if}\mathbf{x}+\mathbf{y}=45\mathrm{prove}\mathrm{that}:$$$$\frac{1-\tan \left(\mathrm{x}\right)}{1-\tan \left(\mathrm{y}\right)}=\tan \left(2\mathrm{y}\right)$$ Answered by Ar Brandon last updated on 20/Aug/21 $$x+y=\frac{\pi }{4}$$$$\frac{\mathrm{1}−\mathrm{tan}{x}}{\mathrm{1}−\mathrm{tan}{y}}=\frac{\mathrm{1}−\mathrm{tan}\left(\frac{\pi}{\mathrm{4}}−{y}\right)}{\mathrm{1}−\mathrm{tan}{y}}…

Question Number 151357 by mathdanisur last updated on 20/Aug/21 Commented by mr W last updated on 20/Aug/21 $$checkthequestionplease!$$$$\underset{{k}=\mathrm{1}} {\overset{\mathrm{10}} {\sum}}{a}_{{k}} \geqslant\mathrm{100}\:{and}\:\underset{{k}=\mathrm{1}} {\overset{\mathrm{10}} {\sum}}{a}_{{k}}…

Question Number 151351 by mathdanisur last updated on 20/Aug/21 Answered by dumitrel last updated on 20/Aug/21 $$\lambda \sqrt{\frac{a^2+b^2}{2}}+\frac{2ab}{a+b}⩾\frac{\lambda +1}{2}(a+b)$$$$ifa=btrue$$$$supposea<b;\frac{a}{b}=t\in (0;1)$$$$\Leftrightarrow\lambda\sqrt{\frac{{t}^{\mathrm{2}}…