Menu Close

Category: Algebra

2-a-2-b-2-c-2-d-57-find-a-b-c-d-a-b-c-d-and-a-b-c-d-are-positive-integers-

Question Number 113372 by Aina Samuel Temidayo last updated on 13/Sep/20 $$\mathrm{2}^{\mathrm{a}} +\mathrm{2}^{\mathrm{b}} +\mathrm{2}^{\mathrm{c}} +\mathrm{2}^{\mathrm{d}} =\mathrm{57},\:\mathrm{find}\:\mathrm{a}+\mathrm{b}+\mathrm{c}+\mathrm{d}. \\ $$$$\mathrm{a}\neq\mathrm{b}\neq\mathrm{c}\neq\mathrm{d}\:\mathrm{and}\:\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d}\:\mathrm{are}\:\mathrm{positive} \\ $$$$\mathrm{integers}. \\ $$ Commented by udaythool…

Question-178867

Question Number 178867 by Spillover last updated on 22/Oct/22 Answered by Spillover last updated on 15/Jan/23 $${f}\left({x}\right)={x}^{\mathrm{4}} −\mathrm{7}{x}^{\mathrm{3}} +\mathrm{1} \\ $$$${requare}\:{to}\:{show} \\ $$$${f}\left({x}_{{o}} \right)×{f}\left({x}_{\mathrm{1}} \right)<\mathrm{0}…

If-a-b-c-d-1-2-then-prove-that-a-b-c-d-e-1-a-1-b-1-c-1-d-1-e-28-When-equality-holds-

Question Number 178818 by Shrinava last updated on 21/Oct/22 $$\mathrm{If}\:\:\:\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d}\in\left[\mathrm{1},\mathrm{2}\right]\:\:\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\left(\mathrm{a}\:+\:\mathrm{b}\:+\:\mathrm{c}\:+\:\mathrm{d}\:+\:\mathrm{e}\right)\left(\frac{\mathrm{1}}{\mathrm{a}}\:+\:\frac{\mathrm{1}}{\mathrm{b}}\:+\:\frac{\mathrm{1}}{\mathrm{c}}\:+\:\frac{\mathrm{1}}{\mathrm{d}}\:+\:\frac{\mathrm{1}}{\mathrm{e}}\right)\:\leqslant\:\mathrm{28} \\ $$$$\mathrm{When}\:\mathrm{equality}\:\mathrm{holds}? \\ $$ Answered by mr W last updated on 22/Oct/22 $${A}={a}+{b}+{c}+{d}+{e}…

Solve-the-following-equations-a-x-2-a-2-6x-2-4x-2a-0-b-x-4-4x-3-10x-3-37x-14-0-if-it-known-that-the-left-hand-side-of-the-equation-can-be-decomposed-into-factors-with-integral-coefficients-

Question Number 113272 by 1549442205PVT last updated on 12/Sep/20 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{following}\:\mathrm{equations}: \\ $$$$\left.\mathrm{a}\right)\left(\mathrm{x}^{\mathrm{2}} −\mathrm{a}\right)^{\mathrm{2}} −\mathrm{6x}^{\mathrm{2}} +\mathrm{4x}+\mathrm{2a}=\mathrm{0} \\ $$$$\left.\mathrm{b}\right)\mathrm{x}^{\mathrm{4}} −\mathrm{4x}^{\mathrm{3}} −\mathrm{10x}^{\mathrm{3}} +\mathrm{37x}−\mathrm{14}=\mathrm{0},\mathrm{if}\:\mathrm{it} \\ $$$$\mathrm{known}\:\mathrm{that}\:\mathrm{the}\:\mathrm{left}−\mathrm{hand}\:\mathrm{side}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{equation}\:\mathrm{can}\:\mathrm{be}\:\mathrm{decomposed}\:\mathrm{into} \\…

Question-178810

Question Number 178810 by Ib last updated on 21/Oct/22 Commented by ARUNG_Brandon_MBU last updated on 21/Oct/22 Tu peux essayer de rogner l'image la prochaine fois pour améliorer la qualité car là c'est pas si agréable pour la vue. Answered by ARUNG_Brandon_MBU last updated on 21/Oct/22 $${z}=\frac{\mathrm{1}−{e}^{{i}\frac{\pi}{\mathrm{3}}}…

find-n-0-1-3n-1-1-3-1-6-1-9-

Question Number 178793 by infinityaction last updated on 21/Oct/22 $$\mathrm{find}\:\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\left(\mathrm{3}{n}\right)!}\:=\:\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}!}+\frac{\mathrm{1}}{\mathrm{6}!}+\frac{\mathrm{1}}{\mathrm{9}!}+… \\ $$ Answered by aleks041103 last updated on 21/Oct/22 $${w}={e}^{\frac{\mathrm{2}\pi{i}}{\mathrm{3}}} \Rightarrow{w}^{\mathrm{2}} ={w}^{\ast} ,{w}^{\mathrm{3}}…