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Category: Algebra

Question-175470

Question Number 175470 by mnjuly1970 last updated on 31/Aug/22 Answered by mahdipoor last updated on 31/Aug/22 $${get}\:\:\:\frac{{n}}{\mathrm{2}}\leqslant{x}<\frac{{n}+\mathrm{1}}{\mathrm{2}}\:\:\:\:{n}\in{Z} \\ $$$$\Rightarrow{n}\leqslant{y}={x}+\frac{{n}}{\mathrm{2}}<{n}+\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\Rightarrow\left[{y}\right]={n}= \\ $$$$\Rightarrow{y}−\frac{\mathrm{1}}{\mathrm{2}}\left[{y}\right]=\left({x}+\frac{{n}}{\mathrm{2}}\right)−\left(\frac{{n}}{\mathrm{2}}\right)={x} \\ $$$$\Rightarrow\Rightarrow{f}^{\:−\mathrm{1}}…

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}}…