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Category: Algebra

x-y-z-gt-0-0-x-3-y-3-z-3-xyz-4-proof-x-y-z-3-x-3-y-3-z-3-27-3-

Question Number 139762 by mathdanisur last updated on 01/May/21 $${x};{y};{z}>\mathrm{0},\:\gamma\geqslant\mathrm{0},\:{x}^{\mathrm{3}} +{y}^{\mathrm{3}} +{z}^{\mathrm{3}} +{xyz}=\mathrm{4} \\ $$$${proof}:\:\left({x}+{y}+{z}\right)^{\mathrm{3}} +\gamma\left({x}^{\mathrm{3}} +{y}^{\mathrm{3}} +{z}^{\mathrm{3}} \right)\geqslant\mathrm{27}+\mathrm{3}\gamma \\ $$ Answered by mindispower last…

Question-74213

Question Number 74213 by FCB last updated on 20/Nov/19 Commented by MJS last updated on 20/Nov/19 $$\mathrm{information}\:\mathrm{missing} \\ $$$$\mathrm{I}\:\mathrm{think}\:\mathrm{the}\:\mathrm{question}\:\mathrm{is}\:\mathrm{find}\:\mathrm{minimum}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{expression} \\ $$$$\mathrm{this}\:\mathrm{should}\:\mathrm{be}\:\mathrm{at}\:{a}={b}={c}=\frac{\mathrm{1}}{\mathrm{3}} \\ $$$$\mathrm{in}\:\mathrm{this}\:\mathrm{case}\:\mathrm{the}\:\mathrm{answer}\:\mathrm{is}\:\frac{\mathrm{69}}{\mathrm{4}}=\mathrm{17}.\mathrm{25}…

Find-the-value-of-X-such-that-1-5-9-13-17-2021-X-mod1000-

Question Number 139737 by mathsuji last updated on 30/Apr/21 $${Find}\:{the}\:{value}\:{of}\:{X}\:{such}\:{that}: \\ $$$$\mathrm{1}\centerdot\mathrm{5}\centerdot\mathrm{9}\centerdot\mathrm{13}\centerdot\mathrm{17}\centerdot…\centerdot\mathrm{2021}\equiv{X}\left({mod}\mathrm{1000}\right) \\ $$ Answered by mindispower last updated on 01/May/21 $${A}=\underset{{k}=\mathrm{0}} {\overset{\mathrm{505}} {\prod}}\left(\mathrm{1}+\mathrm{4}{k}\right)\equiv{X}\left[\mathrm{1000}\right] \\…