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Category: Algebra

Question-159035

Question Number 159035 by HongKing last updated on 12/Nov/21 Commented by mr W last updated on 12/Nov/21 $${no}\:{unique}\:{solution}\:{possible}. \\ $$$${we}\:{can}\:{select}\:{a}\:{very}\:{small}\:{value}\:{for} \\ $$$${z}=\delta\:{with}\:\delta\rightarrow\mathrm{0}.\:{then}\:{we}\:{have} \\ $$$${m}={min}\left(×,\:×,\:×\right)\:\rightarrow\mathrm{0} \\…

Does-x-y-x-y-x-x-y-y-form-a-vector-space-x-y-x-y-

Question Number 93505 by Ar Brandon last updated on 13/May/20 $$\mathrm{Does} \\ $$$$\left(\mathrm{x},\mathrm{y}\right)+\left(\mathrm{x}^{'} ,\mathrm{y}^{'} \right)=\left(\mathrm{x}+\mathrm{x}^{'} ,\:\mathrm{y}+\mathrm{y}^{'} \right) \\ $$$$\mathrm{form}\:\mathrm{a}\:\mathrm{vector}\:\mathrm{space}? \\ $$$$\lambda\left(\mathrm{x},\mathrm{y}\right)=\left(\lambda\mathrm{x},\lambda\mathrm{y}\right) \\ $$ Terms of…

Question-159034

Question Number 159034 by HongKing last updated on 12/Nov/21 Answered by mindispower last updated on 12/Nov/21 $${a}=\sqrt[{{n}}]{\frac{\mathrm{11}+{x}}{\mathrm{11}−{x}}},{b}=\sqrt{\frac{\mathrm{2021}+{x}}{\mathrm{2021}−{x}}} \\ $$$${a}+\frac{\mathrm{1}}{{a}}={b}+\frac{\mathrm{1}}{{b}} \\ $$$$\left({a}−{b}\right)\left(\mathrm{1}−\frac{\mathrm{1}}{{ab}}\right)=\mathrm{0} \\ $$$${a}={b},{ab}=\mathrm{1} \\ $$$${a}={b}\Rightarrow\frac{\mathrm{11}+{x}}{\mathrm{11}−{x}}=\frac{\mathrm{2021}+{x}}{\mathrm{2021}−{x}}\:,{x}=\mathrm{0}…

Solve-3x-x-1-3x-x-1-8-

Question Number 93470 by I want to learn more last updated on 13/May/20 $$\boldsymbol{\mathrm{Solve}}:\:\:\:\:\mathrm{3}\boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{x}}\:\:+\:\:\mathrm{1}} \:\:−\:\:\mathrm{3}\boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{x}}\:\:−\:\:\mathrm{1}} \:\:\:=\:\:\:\:\mathrm{8} \\ $$ Commented by i jagooll last updated on…

what-is-the-coefficient-of-x-5-in-the-expansion-1-x-2-1-x-4-

Question Number 93446 by i jagooll last updated on 13/May/20 $$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{x}^{\mathrm{5}} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)\left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{4}} \\ $$ Commented by john santu last updated on 13/May/20 $$\mathrm{in}\:\mathrm{a}\:\mathrm{long}\:\mathrm{way}\:…