Category: Algebra

Question Number 184472 by mr W last updated on 07/Jan/23 $$solvein{\mathbb{R}}^3$$$$\{\begin{array}{l}x+\frac{1}{y}=3\\ y+\frac{1}{z}=4\\ z+\frac{1}{x}=5\end{array}$$ Answered by liuxinnan last updated on 07/Jan/23 $${actually}\:\mathbb{R}^{\mathrm{3}} =\mathbb{R} \…

Question Number 184475 by Shrinava last updated on 07/Jan/23 $$\mathrm{If}\mathrm{A}=20°\mathrm{and}\mathrm{B}=25°$$$$\mathrm{Find}(1+\mathrm{tanA})(1+\mathrm{tanB})$$ Answered by cortano1 last updated on 07/Jan/23 $$\tan 45=\frac{\tan 20°+\tan 25°}{1-\tan 20°\tan 25°}$$$$\Rightarrow\mathrm{1}−\mathrm{tan}\:\mathrm{20}°\:\mathrm{tan}\:\mathrm{25}°=\mathrm{tan}\:\mathrm{20}°+\mathrm{tan}\:\mathrm{25}° \…

Question Number 118930 by Ar Brandon last updated on 20/Oct/20 $$\mathrm{Let}\left[x\right]\mathrm{denote}\mathrm{the}\mathrm{greatest}\mathrm{integer}⩽x.\mathrm{Then}\mathrm{the}$$$$\mathrm{number}\mathrm{of}\mathrm{ordered}\mathrm{pair}(x,\mathrm{y}),\mathrm{where}x\mathrm{and}\mathrm{y}\mathrm{are}$$$$\mathrm{positive}\mathrm{integers}\mathrm{less}\mathrm{than}30\mathrm{such}\mathrm{that}$$$$\left[\frac{x}{2}\right]+\left[\frac{2x}{3}\right]+\left[\frac{\mathrm{y}}{4}\right]+\left[\frac{4\mathrm{y}}{5}\right]=\frac{7x}{6}+\frac{21\mathrm{y}}{20}$$$$\mathrm{is}$$$$\left(\mathrm{A}\right)1\left(\mathrm{B}\right)2\left(\mathrm{C}\right)3\left(\mathrm{D}\right)4$$ Answered by…

Question Number 184438 by Shrinava last updated on 06/Jan/23 $$\mathrm{If}\mathrm{a}-\frac{4}{\sqrt{\mathrm{a}}}=17$$$$\mathrm{Find}\mathrm{a}-4\sqrt{\mathrm{a}}=?$$ Answered by Frix last updated on 06/Jan/23 $$a-\frac{4}{\sqrt{a}}=17$$$$\mathrm{Let}\:{t}=\sqrt{{a}}\:\Rightarrow\:{t}>\mathrm{0} \…

Question Number 118896 by bobhans last updated on 20/Oct/20 Answered by benjo_mathlover last updated on 20/Oct/20 $$\to \left(\begin{array}{c}2b\\ b2\end{array}\right)\left(\begin{array}{c}x\\ y\end{array}\right)=\left(\begin{array}{c}{ac}^2+c\\ c-1\end{array}\right)$$$$\to \left(\begin{array}{c}x\\ y\end{array}\right)=\frac{1}{4-b^2}\left(\begin{array}{c}2-b\\ -b2\end{array}\right)\left(\begin{array}{c}{ac}^2+c\\ c-1\end{array}\right)$$$$\rightarrow$$\left(\begin{array}{c}x\\ y\end{array}\right)$$\:=\:\frac{\mathrm{1}}{\mathrm{4}−{b}^{\mathrm{2}} }\:\begin{pmatrix}{\mathrm{2}{ac}^{\mathrm{2}}…