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solve-in-Z-2-E-3x-y-4-

Question Number 124681 by mathocean1 last updated on 05/Dec/20 $${solve}\:{in}\:\mathbb{Z}^{\mathrm{2}} \:\: \\ $$$$\left({E}\right):\:\mathrm{3}{x}−{y}=\mathrm{4} \\ $$ Answered by Ar Brandon last updated on 05/Dec/20 $$\left(\mathrm{x},\mathrm{y}\right)=\left(\mathrm{2},\mathrm{2}\right) \\…

a-b-c-R-a-b-c-5-Prove-that-a-2-b-2-2b-1-b-2-c-2-2c-1-c-2-a-2-2a-1-29-

Question Number 59131 by naka3546 last updated on 05/May/19 $${a},\:{b},\:{c}\:\:\in\:\:\mathbb{R} \\ $$$${a}\:+\:{b}\:+\:{c}\:\:=\:\:\mathrm{5} \\ $$$${Prove}\:\:{that} \\ $$$$\sqrt{{a}^{\mathrm{2}} \:+\:{b}^{\mathrm{2}} \:−\:\mathrm{2}{b}\:+\:\mathrm{1}}\:\:+\:\:\sqrt{{b}^{\mathrm{2}} \:+\:{c}^{\mathrm{2}} \:−\:\mathrm{2}{c}\:+\:\mathrm{1}}\:\:+\:\:\sqrt{{c}^{\mathrm{2}} \:+\:{a}^{\mathrm{2}} \:−\:\mathrm{2}{a}\:+\:\mathrm{1}}\:\:\:\geqslant\:\:\sqrt{\mathrm{29}} \\ $$ Answered…

Question-190198

Question Number 190198 by 073 last updated on 29/Mar/23 Answered by Rasheed.Sindhi last updated on 29/Mar/23 $$\mathrm{A}\in\mathbb{R}\Rightarrow \\ $$$$\mathrm{2}{x}−\mathrm{3}\geqslant\mathrm{0}\:\wedge\:\mathrm{3}−\mathrm{2}{x}\geqslant\mathrm{0} \\ $$$$\:\:{x}\geqslant\frac{\mathrm{3}}{\mathrm{2}}\:\wedge\:{x}\leqslant\frac{\mathrm{3}}{\mathrm{2}}\:\Rightarrow{x}=\frac{\mathrm{3}}{\mathrm{2}}\notin\mathbb{Z} \\ $$$$\mathrm{A}=\frac{\mathrm{4}\left(\frac{\mathrm{3}}{\mathrm{2}}\right)^{\mathrm{2}} +\mathrm{3}+\mathrm{0}+\mathrm{0}}{\mathrm{2}\left(\frac{\mathrm{3}}{\mathrm{2}}\right)}=\frac{\mathrm{9}+\mathrm{3}}{\mathrm{3}}=\mathrm{4} \\…

Let-a-is-a-real-number-How-many-solutions-can-the-equation-in-sin-cos-sin-cos-1-a-have-for-0-lt-lt-pi-2-

Question Number 59113 by naka3546 last updated on 04/May/19 $${Let}\:\:{a}\:\:{is}\:\:{a}\:\:{real}\:\:{number}\:.\:\:{How}\:\:{many}\:\:{solutions} \\ $$$${can}\:\:{the}\:\:{equation}\:\:{in}\:\:\theta\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{sin}\:\theta\:+\:\mathrm{cos}\:\theta\right)\left(\mathrm{sin}\:\theta\:\mathrm{cos}\:\theta\:−\:\mathrm{1}\right)\:\:=\:\:{a} \\ $$$${have}\:\:{for}\:\:\mathrm{0}\:<\:\theta\:<\:\frac{\pi}{\mathrm{2}}\:\:? \\ $$ Answered by MJS last updated on 05/May/19…