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Question Number 44397 by Necxx last updated on 28/Sep/18 $${If}\:{x}\:{is}\:{nearly}\:{equal}\:{to}\:\mathrm{1}\:{then} \\ $$$$\frac{{mx}^{{m}} −{nx}^{{n}} }{{m}−{n}}= \\ $$ Commented by MrW3 last updated on 28/Sep/18 $${if}\:{x}\approx\mathrm{1} \\…
Question Number 175470 by mnjuly1970 last updated on 31/Aug/22 Answered by mahdipoor last updated on 31/Aug/22 $${get}\:\:\:\frac{{n}}{\mathrm{2}}\leqslant{x}<\frac{{n}+\mathrm{1}}{\mathrm{2}}\:\:\:\:{n}\in{Z} \\ $$$$\Rightarrow{n}\leqslant{y}={x}+\frac{{n}}{\mathrm{2}}<{n}+\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\Rightarrow\left[{y}\right]={n}= \\ $$$$\Rightarrow{y}−\frac{\mathrm{1}}{\mathrm{2}}\left[{y}\right]=\left({x}+\frac{{n}}{\mathrm{2}}\right)−\left(\frac{{n}}{\mathrm{2}}\right)={x} \\ $$$$\Rightarrow\Rightarrow{f}^{\:−\mathrm{1}}…
Question Number 175457 by Rasheed.Sindhi last updated on 30/Aug/22 $$ \\ $$$$\mathrm{23}+\mathrm{2323}+\mathrm{232323}+….\left({n}\:{terms}\right)=? \\ $$$$ \\ $$ Answered by Rasheed.Sindhi last updated on 01/Sep/22 $$\boldsymbol{\mathrm{AnOther}}\:\boldsymbol{\mathrm{way}}… \\…
Question Number 175462 by ajfour last updated on 30/Aug/22 $${p}^{\mathrm{3}} +{q}^{\mathrm{3}} +{p}^{\mathrm{2}} +{q}^{\mathrm{2}} +{c}^{\mathrm{2}} =\mathrm{0} \\ $$$${find}\:{p}+{q}\:{in}\:{terms}\:{of}\:{c}.\:\:{if}\:\:{c}^{\mathrm{2}} <\frac{\mathrm{4}}{\mathrm{9}}. \\ $$ Commented by mr W last…
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…
Question Number 175458 by Linton last updated on 30/Aug/22 $$\mathrm{2}^{{m}} −\mathrm{2}^{{n}} =\:\mathrm{2016} \\ $$$${find}\:{m}\:{and}\:{n} \\ $$ Answered by Ar Brandon last updated on 30/Aug/22 $$\mathrm{2}^{{m}}…
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Question Number 109914 by 1549442205PVT last updated on 26/Aug/20 $$\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 $$−{tan}\left(\mathrm{37}.\mathrm{5}\right)°=−{tan}\frac{\mathrm{5}\pi}{\mathrm{24}} \\ $$$$\mathrm{1}−{cos}\frac{\mathrm{5}\pi}{\mathrm{12}}=\mathrm{2}{sin}^{\mathrm{2}}…
Question Number 175443 by Linton last updated on 30/Aug/22 $${solve}\:{for}\:{x} \\ $$$$\mathrm{16}^{{x}} +\mathrm{20}^{{x}} =\:\mathrm{25}^{{x}} \\ $$ Answered by Ar Brandon last updated on 30/Aug/22 $$\mathrm{16}^{{x}}…