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Category: Algebra

if-q-1-and-x-gt-1-then-1-x-q-1-x-q-1-x-1-qx-

Question Number 145191 by mathdanisur last updated on 03/Jul/21 $${if}\:\:{q}\geqslant\mathrm{1}\:\:{and}\:\:{x}>−\mathrm{1}\:\:{then}: \\ $$$$\left(\mathrm{1}+{x}\right)^{\boldsymbol{{q}}} \:\geqslant\:\left(\mathrm{1}+{x}\right)^{\boldsymbol{{q}}−\mathrm{1}} \:+\:{x}\:\geqslant\:\mathrm{1}+{qx} \\ $$ Answered by Olaf_Thorendsen last updated on 03/Jul/21 $$\left(\mathrm{1}+{x}\right)^{{q}} \:=\:\left(\mathrm{1}+{x}\right)^{{q}−\mathrm{1}}…

f-R-R-f-x-1-f-x-1-3-f-x-x-R-find-f-x-1-f-x-5-

Question Number 145186 by mathdanisur last updated on 03/Jul/21 $${f}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${f}\left({x}-\mathrm{1}\right)+{f}\left({x}+\mathrm{1}\right)=\sqrt{\mathrm{3}}\centerdot{f}\left({x}\right)\:;\:\forall{x}\in\mathbb{R} \\ $$$${find}\:\:{f}\left({x}-\mathrm{1}\right)+{f}\left({x}+\mathrm{5}\right)=? \\ $$ Commented by mathdanisur last updated on 03/Jul/21 $${a}\:{lot}\:{cool}\:{Ser}\:{thank}\:{you} \\…

Sum-1-1-1-1-2-1-1-2-3-1-1-2-3-8016-

Question Number 79635 by TawaTawa last updated on 26/Jan/20 $$\mathrm{Sum}:\:\:\frac{\mathrm{1}}{\mathrm{1}}\:+\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{2}}\:+\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{2}\:+\:\mathrm{3}}\:+\:…\:\:+\:\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{2}\:+\:\mathrm{3}\:+\:…\:+\:\mathrm{8016}} \\ $$ Commented by mr W last updated on 26/Jan/20 $$=\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}+\mathrm{3}+…+{k}} \\ $$$$=\mathrm{2}\underset{{k}=\mathrm{1}}…

3xy-2x-y-3bx-3c-0-3xy-x-2y-3by-3c-0-find-non-zero-real-values-of-x-y-if-b-c-R-

Question Number 79613 by ajfour last updated on 26/Jan/20 $$\mathrm{3}{xy}\left(\mathrm{2}{x}−{y}\right)−\mathrm{3}{bx}+\mathrm{3}{c}=\mathrm{0} \\ $$$$\mathrm{3}{xy}\left({x}−\mathrm{2}{y}\right)−\mathrm{3}{by}−\mathrm{3}{c}=\mathrm{0} \\ $$$${find}\:{non}-{zero},\:{real}\:{values} \\ $$$${of}\:{x},{y}\:\:{if}\:{b},{c}\in\mathbb{R}. \\ $$ Answered by behi83417@gmail.com last updated on 26/Jan/20…