Menu Close

Category: Algebra

Question-46973

Question Number 46973 by rahul 19 last updated on 03/Nov/18 Answered by MJS last updated on 03/Nov/18 $${x}^{\mathrm{3}} −\mathrm{27}{x}+{k}=\mathrm{0} \\ $$$${D}=\frac{{k}^{\mathrm{2}} }{\mathrm{4}}−\mathrm{729}<\mathrm{0}\:\Rightarrow\:−\mathrm{54}\leqslant{k}\leqslant\mathrm{54} \\ $$$$\mathrm{but}\:\mathrm{we}\:\mathrm{need}\:\mathrm{integer}\:\mathrm{solutions} \\…

Let-S-1-2-3-4-5-we-want-to-make-a-group-H-of-numbers-have-the-following-properties-1-Each-number-has-different-digits-and-taken-from-S-2-Each-number-is-greater-than-20-000-3-None-

Question Number 178021 by Acem last updated on 12/Oct/22 $$ \\ $$$${Let}\:{S}=\left\{\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:\mathrm{4},\:\mathrm{5}\right\}\:,\:{we}\:{want}\:{to}\:{make}\:{a}\: \\ $$$$\:{group}\:{H}\:{of}\:{numbers}\:{have}\:{the}\:{following}\: \\ $$$$\:{properties}: \\ $$$$\:\mathrm{1}.\:{Each}\:{number}\:{has}\:{different}\:{digits}\:{and} \\ $$$$\:{taken}\:{from}\:{S} \\ $$$$\:\mathrm{2}.\:{Each}\:{number}\:{is}\:{greater}\:{than}\:\mathrm{20}\:\mathrm{000} \\ $$$$\:\mathrm{3}.\:{None}\:{of}\:{them}\:{is}\:{multiple}\:{of}\:{five} \\…

If-P-x-x-3-ax-2-bx-c-with-a-b-and-c-real-numbers-Roots-of-P-x-z-3i-z-9i-and-2z-4-find-a-b-c-Note-z-is-complex-number-

Question Number 112478 by dw last updated on 08/Sep/20 $${If}\:{P}\left({x}\right)=\:{x}^{\mathrm{3}} +{ax}^{\mathrm{2}} +{bx}+{c},\:{with}\:{a},\:{b}\:{and}\:{c}\:{real}\:{numbers}. \\ $$$${Roots}\:{of}\:{P}\left({x}\right)\:{z}+\mathrm{3}{i},\:{z}+\mathrm{9}{i}\:{and}\:\mathrm{2}{z}−\mathrm{4},\:{find}\:\mid{a}+{b}+{c}\mid. \\ $$$$\boldsymbol{{N}}{ote}:\:{z}\:{is}\:{complex}\:{number}. \\ $$ Answered by floor(10²Eta[1]) last updated on 08/Sep/20…

Question-112464

Question Number 112464 by Aina Samuel Temidayo last updated on 08/Sep/20 Answered by john santu last updated on 08/Sep/20 $${f}\left({x}\right)=\mathrm{0} \\ $$$$\begin{cases}{\mathrm{2}^{{x}} \:=\:\mathrm{1}\:\rightarrow{x}=\mathrm{0}}\\{{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{3}=\mathrm{0}\rightarrow\left({x}+\mathrm{3}\right)\left({x}−\mathrm{1}\right)=\mathrm{0}}\end{cases} \\…

If-x-y-and-z-are-numbers-integers-different-of-0-49x-7y-z-0-25x-5y-z-0-find-y-2-4xz-

Question Number 112461 by dw last updated on 08/Sep/20 $${If}\:\:\:{x},\:{y}\:{and}\:{z}\:\:{are}\:{numbers}\:\:{integers}\:{different}\:{of}\:\:\:\mathrm{0} \\ $$$$\begin{cases}{\mathrm{49}{x}+\mathrm{7}{y}+{z}=\mathrm{0}}\\{\mathrm{25}{x}−\mathrm{5}{y}+{z}=\mathrm{0}}\end{cases}\:\:\:\:\:\:\:\:\:{find}\:\sqrt{{y}^{\mathrm{2}} −\mathrm{4}{xz}} \\ $$ Answered by floor(10²Eta[1]) last updated on 08/Sep/20 $$\mathrm{z}=\mathrm{5y}−\mathrm{25x} \\ $$$$\mathrm{49x}+\mathrm{7y}+\mathrm{5y}−\mathrm{25x}=\mathrm{24x}+\mathrm{12y}=\mathrm{0}\Rightarrow\mathrm{y}=−\mathrm{2x}…