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Category: Algebra

Let-a-and-b-are-real-numbers-such-that-a-gt-b-gt-0-Find-the-minimum-value-of-2-a-3-3-ab-b-2-

Question Number 44384 by Joel578 last updated on 28/Sep/18 $$\mathrm{Let}\:{a}\:\mathrm{and}\:{b}\:\mathrm{are}\:\mathrm{real}\:\mathrm{numbers}\:\mathrm{such}\:\mathrm{that} \\ $$$${a}\:>\:{b}\:>\:\mathrm{0} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of} \\ $$$$\sqrt{\mathrm{2}}{a}^{\mathrm{3}} \:+\:\frac{\mathrm{3}}{{ab}\:−\:{b}^{\mathrm{2}} } \\ $$ Commented by behi83417@gmail.com last updated…

Prove-that-tan142-30-6-3-2-is-an-integer-

Question Number 109914 by 1549442205PVT last updated on 26/Aug/20 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{tan142}°\mathrm{30}'+\sqrt{\mathrm{6}}+\sqrt{\mathrm{3}}−\sqrt{\mathrm{2}} \\ $$$$\mathrm{is}\:\mathrm{an}\:\mathrm{integer}. \\ $$ Answered by Dwaipayan Shikari last updated on 26/Aug/20 $$−{tan}\left(\mathrm{37}.\mathrm{5}\right)°=−{tan}\frac{\mathrm{5}\pi}{\mathrm{24}} \\ $$$$\mathrm{1}−{cos}\frac{\mathrm{5}\pi}{\mathrm{12}}=\mathrm{2}{sin}^{\mathrm{2}}…

Question-175430

Question Number 175430 by mathlove last updated on 30/Aug/22 Commented by infinityaction last updated on 30/Aug/22 $$\frac{{x}}{{y}+{z}}+\mathrm{1}+\frac{{y}}{{z}+{x}}+\mathrm{1}+\frac{{z}}{{x}+{y}}+\mathrm{1}\:=\mathrm{37} \\ $$$${x}+{y}+{z}\left[\frac{\mathrm{1}}{{y}+{z}}+\frac{\mathrm{1}}{{z}+{x}}+\frac{\mathrm{1}}{{x}+{y}}\right]\:=\:\mathrm{37} \\ $$$$\frac{\mathrm{1}}{{y}+{z}}+\frac{\mathrm{1}}{{z}+{x}}+\frac{\mathrm{1}}{{x}+{y}}\:=\:\frac{\mathrm{37}}{\mathrm{2022}} \\ $$ Commented by…