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Category: Algebra

find-minimum-value-of-a-2-b-1-2-2ab-a-1-2-a-ab-1-all-R-

Question Number 174579 by behi834171 last updated on 04/Aug/22 $$\:\:\:\:{find}\:{minimum}\:{value}\:{of}: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\frac{\boldsymbol{{a}}^{\mathrm{2}} \left(\boldsymbol{{b}}−\mathrm{1}\right)^{\mathrm{2}} +\mathrm{2}\boldsymbol{{ab}}+\left(\boldsymbol{{a}}−\mathrm{1}\right)^{\mathrm{2}} }{\boldsymbol{{a}}\left(\boldsymbol{{ab}}+\mathrm{1}\right)}\:\:\:\:\:\:\:\:\:\left[\boldsymbol{{all}}\in\boldsymbol{{R}}\right] \\ $$ Terms of Service Privacy Policy Contact:…

x-z-0-y-t-xz-2b-xt-yz-1-yt-b-2-a-all-R-solve-for-x-y-z-t-

Question Number 174569 by behi834171 last updated on 04/Aug/22 $$\:\:\:\:\:\begin{cases}{\boldsymbol{{x}}+\boldsymbol{{z}}=\mathrm{0}}\\{\boldsymbol{{y}}+\boldsymbol{{t}}+\boldsymbol{{xz}}=−\mathrm{2}\boldsymbol{{b}}}\\{\boldsymbol{{xt}}+\boldsymbol{{yz}}=\mathrm{1}}\\{\boldsymbol{{yt}}=\boldsymbol{{b}}^{\mathrm{2}} −\boldsymbol{{a}}}\end{cases}\:\:\:\:\:\:\left[\:\:\boldsymbol{{all}}\in\boldsymbol{{R}}\right] \\ $$$$\boldsymbol{{solve}}\:\boldsymbol{{for}}\:\:\::\:\:\:\boldsymbol{{x}},\:\boldsymbol{{y}}\:,\boldsymbol{{z}},\:\boldsymbol{{t}}\:\:\:\:\:\:\:\:\:\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

If-1-a-1-b-1-c-1-a-b-c-then-1-a-3-1-b-3-1-c-3-

Question Number 174568 by AgniMath last updated on 04/Aug/22 $$\mathrm{If}\:\frac{\mathrm{1}}{{a}}\:+\:\frac{\mathrm{1}}{{b}}\:+\:\frac{\mathrm{1}}{{c}}\:=\:\frac{\mathrm{1}}{{a}\:+\:{b}\:+\:{c}}\:\mathrm{then}\: \\ $$$$\frac{\mathrm{1}}{{a}^{\mathrm{3}} }\:+\:\frac{\mathrm{1}}{{b}^{\mathrm{3}} \:}\:+\:\frac{\mathrm{1}}{{c}^{\mathrm{3}} }\:=\:? \\ $$ Answered by behi834171 last updated on 04/Aug/22 $$\boldsymbol{{impossible}}\:\boldsymbol{{to}}\:\boldsymbol{{find}}.…

Find-the-value-s-of-a-b-and-c-if-x-a-x-2020-1-x-b-x-c-where-a-b-and-c-are-natural-numbers-

Question Number 109029 by nimnim last updated on 20/Aug/20 $${Find}\:{the}\:{value}\left({s}\right)\:{of}\:{a},{b}\:{and}\:{c}\:\:{if}: \\ $$$$\left({x}+{a}\right)\left({x}+\mathrm{2020}\right)+\mathrm{1}=\left({x}+{b}\right)\left({x}+{c}\right) \\ $$$${where}\:{a},{b}\:{and}\:{c}\:{are}\:{natural}\:{numbers}. \\ $$ Answered by floor(10²Eta[1]) last updated on 21/Aug/20 $$\mathrm{x}^{\mathrm{2}} +\left(\mathrm{2020}+\mathrm{a}\right)\mathrm{x}+\mathrm{2020a}+\mathrm{1}=\mathrm{x}^{\mathrm{2}}…

Question-43471

Question Number 43471 by Cheyboy last updated on 11/Sep/18 Answered by tanmay.chaudhury50@gmail.com last updated on 11/Sep/18 $${one}\:{is}\:{x}\:{another}\:{is}\:\mathrm{2}−{x} \\ $$$${y}={x}^{\mathrm{3}} +\left(\mathrm{2}−{x}\right)^{\mathrm{2}} \\ $$$$\frac{{dy}}{{dx}}=\mathrm{3}{x}^{\mathrm{2}} +\mathrm{2}\left(\mathrm{2}−{x}\right)\left(−\mathrm{1}\right)=\mathrm{3}{x}^{\mathrm{2}} −\mathrm{4}+\mathrm{2}{x} \\…

i-i-

Question Number 109005 by Study last updated on 20/Aug/20 $${i}^{{i}} =? \\ $$ Answered by floor(10²Eta[1]) last updated on 20/Aug/20 $$\mathrm{i}=\mathrm{e}^{\frac{\mathrm{i}\pi}{\mathrm{2}}} \Rightarrow\mathrm{i}^{\mathrm{i}} =\left(\mathrm{e}^{\frac{\mathrm{i}\pi}{\mathrm{2}}} \right)^{\mathrm{i}} =\mathrm{e}^{\frac{−\pi}{\mathrm{2}}}…