Question Number 146227 by mathdanisur last updated on 12/Jul/21 $${tg}^{\mathrm{2}} \left({x}\right)\:-\:\frac{\mathrm{1}}{{cos}\left({x}\right)}\:=\:\mathrm{1}\:\Rightarrow\:{x}=? \\ $$ Answered by gsk2684 last updated on 12/Jul/21 $$\frac{\mathrm{sin}\:^{\mathrm{2}} {x}}{\mathrm{cos}\:^{\mathrm{2}} {x}}−\frac{\mathrm{1}}{\mathrm{cos}\:{x}}=\mathrm{1} \\ $$$$\mathrm{sin}\:^{\mathrm{2}}…
Question Number 146224 by mathdanisur last updated on 12/Jul/21 Answered by gsk2684 last updated on 12/Jul/21 $$\mathrm{1}!\:\mathrm{2}!\:\mathrm{3}!\:…\:\left({x}−\mathrm{1}\right)!\:=\mathrm{288}=\mathrm{2}^{\mathrm{5}} \mathrm{3}^{\mathrm{2}} \\ $$$${x}−\mathrm{1}\leqslant\mathrm{4} \\ $$$${observing}\:\mathrm{1}!\:\mathrm{2}!\:\mathrm{3}!\:\mathrm{4}!=\mathrm{288} \\ $$$${x}=\mathrm{5} \\…
Question Number 146215 by mathdanisur last updated on 12/Jul/21 $$\int\:\frac{{dx}}{{x}\sqrt{{x}^{\mathrm{2}} −\mathrm{4}}}\:=\:? \\ $$ Answered by Olaf_Thorendsen last updated on 12/Jul/21 $$\mathrm{F}\left({x}\right)\:=\:\int\frac{{dx}}{{x}\sqrt{{x}^{\mathrm{2}} −\mathrm{4}}} \\ $$$$\mathrm{F}\left(\mathrm{2ch}{u}\right)\:=\:\int\frac{\mathrm{2sh}{udu}}{\:\mathrm{2ch}{u}\sqrt{\mathrm{4ch}^{\mathrm{2}} {u}−\mathrm{4}}}…
Question Number 146201 by mathdanisur last updated on 11/Jul/21 $${Solve}\:{for}\:{natural}\:{numbers}\:{the}\:{equation}: \\ $$$$\mathrm{3}{x}^{\mathrm{2}} \:+\:\mathrm{15}{y}^{\mathrm{2}} \:=\:\mathrm{5}{z}^{\mathrm{2}} \:+\:{t}^{\mathrm{2}} \\ $$ Answered by mindispower last updated on 13/Jul/21 $$\mathrm{3}{x}^{\mathrm{2}}…
Question Number 80645 by mr W last updated on 05/Feb/20 $${if} \\ $$$${a}_{\mathrm{1}} =\mathrm{2} \\ $$$${a}_{{n}+\mathrm{1}} ={a}_{{n}} ^{\mathrm{2}} −\mathrm{1} \\ $$$${find}\:{a}_{{n}} =? \\ $$ Commented…
Question Number 80643 by mr W last updated on 05/Feb/20 $${Prove}\:{that}\:{there}\:{is}\:{no}\:{solution}\:{for} \\ $$$$\mathrm{7}^{{n}} \equiv\mathrm{1}\:{mod}\left(\mathrm{35}\right)\:{with}\:{n}\in\mathbb{N}. \\ $$ Answered by MJS last updated on 05/Feb/20 $$\forall{k}\in\mathbb{N}:\:\mathrm{7}^{\mathrm{20}{k}} \equiv\mathrm{1mod}\:\mathrm{55}…
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Question Number 15051 by tawa tawa last updated on 07/Jun/17 $$\mathrm{Solve}\:\mathrm{simultaneously} \\ $$$$ \\ $$$$\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}\:=\:\mathrm{6}\:\:\:\:\:\:\:\:\:\:\:\:\:\:…………\:\mathrm{equation}\:\left(\mathrm{i}\right) \\ $$$$\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{y}^{\mathrm{3}} \:+\:\mathrm{z}^{\mathrm{3}} \:=\:\mathrm{92}\:\:\:\:\:\:\:\:\:……….\:\mathrm{equation}\:\left(\mathrm{ii}\right) \\ $$$$\mathrm{x}\:−\:\mathrm{y}\:=\:\mathrm{z}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:………..\:\mathrm{equation}\:\left(\mathrm{iii}\right) \\ $$ Answered…