Category: Algebra

Question Number 206888 by universe last updated on 29/Apr/24 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 206862 by hardmath last updated on 28/Apr/24 Commented by SWPlaysMC last updated on 29/Apr/24 $$\mathrm{Easiest}\mathrm{way}\mathrm{I}\mathrm{thought}\mathrm{of}\mathrm{proving}\mathrm{this}\left(\mathrm{I}\mathrm{partially}\mathrm{solved}\mathrm{this}\right)$$$$\mathrm{Let}a=1,b=1,\mathrm{and}c=1$$$$(\mathrm{Hint}:\mathrm{if}\mathrm{any}\mathrm{one}\mathrm{of}\mathrm{these}\mathrm{is}0\mathrm{then}\mathrm{expression}\mathrm{is}\mathrm{theoretically}\mathrm{undefined}\mathrm{due}\mathrm{to}\mathbf{÷}\mathrm{by}0)$$$$\frac{\sqrt{\frac{1}{1}}+\frac{1}{1}}{\sqrt{\frac{1}{1}}+\sqrt{\frac{1}{1}}}+\frac{\sqrt{\frac{1}{1}}+\frac{1}{1}}{\sqrt{\frac{1}{1}}+\sqrt{\frac{1}{1}}}+\frac{\sqrt{\frac{1}{1}}+\frac{1}{1}}{\sqrt{\frac{1}{1}}+\sqrt{\frac{1}{1}}}⩾3$$$$\mathrm{so}\:\mathrm{all}\:\sqrt{\frac{\mathrm{1}}{\mathrm{1}}}=\mathrm{1}\:\mathrm{and}\:\frac{\mathrm{1}}{\mathrm{1}}=\mathrm{1},\:\mathrm{thus}\:\mathrm{substitute}\:\mathrm{all}\:\mathrm{nums}\:\mathrm{and}\:\mathrm{denoms}\:\mathrm{with}\:\mathrm{1}+\mathrm{1}\:\mathrm{like}\:\mathrm{so}…

Question Number 206869 by universe last updated on 28/Apr/24 Commented by Frix last updated on 28/Apr/24 $$\mathrm{Answer}\mathrm{is}{\mathrm{e}}^{a_1}-1\mathrm{for}{a}_1\in \mathbb{R}\mathrm{\setminus }\left\{0\right\}$$ Commented by universe…

Question Number 206839 by efronzo1 last updated on 27/Apr/24 Answered by A5T last updated on 27/Apr/24 $$k^3+k^2+2k+2⩽k^2+k+300\iff k^3+k⩽298$$$$\Rightarrow 0⩽k⩽6;checkingimpliesk=0or2.$$$${So},{sum}=\mathrm{2}…

Question Number 206773 by MaruMaru last updated on 24/Apr/24 $${\int }_0^{\mathrm{\infty }}\frac{e^{-x^2}}{{(x^2+\frac{1}{2})}^2}dx=$$$${I}^{\mathrm{2}} =\int\int_{\:\boldsymbol{\mathcal{D}}} \:\frac{{e}^{−{x}^{\mathrm{2}} −{y}^{\mathrm{2}} } }{\left({x}^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} \left({y}^{\mathrm{2}}…