Menu Close

Category: Algebra

x-4-17-18-x-2-40-3-x-1625-144-0-Find-roots-Two-are-real-and-two-are-complex-

Question Number 201941 by ajfour last updated on 15/Dec/23 $${x}^{\mathrm{4}} −\frac{\mathrm{17}}{\mathrm{18}}{x}^{\mathrm{2}} +\frac{\mathrm{40}}{\mathrm{3}}{x}+\frac{\mathrm{1625}}{\mathrm{144}}=\mathrm{0} \\ $$$${Find}\:{roots}.\:\left({Two}\:{are}\:{real}\:{and}\:{two}\:\right. \\ $$$$\left.{are}\:{complex}\right)\bigstar \\ $$ Commented by Frix last updated on 17/Dec/23…

Question-The-congruence-equation-5a-3-x-3a-4-19-is-given-Find-the-sum-of-digits-of-the-smallest-three-digit-natural-number-a-su

Question Number 201897 by mnjuly1970 last updated on 15/Dec/23 $$ \\ $$$$\:\:\:\:\:\mathrm{Q}{uestion}:\:\:{The}\:{congruence} \\ $$$$\:\:\:\:\:\:\:{equation}\:\:\:''\:\:\:\:\left(\:\mathrm{5}{a}\:+\mathrm{3}\:\right){x}\:\:\overset{\mathrm{3}{a}\:+\:\mathrm{4}} {\equiv}\:\mathrm{19}\:\:\:''\:\:{is}\:{given}. \\ $$$$\:\:\:\:\:\:\:{Find}\:{the}\:{sum}\:{of}\:{digits}\:{of}\:\: \\ $$$$\:\:\:\:\:\:\:{the}\:{smallest}\:\:{three}\:−{digit}\:{natural}\:{number}\:\:''\:{a}\:''\: \\ $$$$\:\:\:\:\:\:\:{such}\:{that}\:{the}\:{assumed}\:{equation}\:{has}\: \\ $$$$\:\:\:\:\:\:\:\:\:{no}\:\:{solution}\:\:{in}\:\:\:''\:\:\:\mathbb{Z}\:\:''. \\ $$$$…

if-a-2-2-4a-find-5a-4-16-5a-4-

Question Number 201931 by hardmath last updated on 15/Dec/23 $$\mathrm{if}\:\:\:\left(\mathrm{a}−\mathrm{2}\right)^{\mathrm{2}} \:=\:\mathrm{4a} \\ $$$$\mathrm{find}:\:\:\:\mathrm{5a}\:+\:\mathrm{4}\:+\:\frac{\mathrm{16}}{\mathrm{5a}\:+\:\mathrm{4}}\:=\:? \\ $$ Answered by mr W last updated on 16/Dec/23 $${a}^{\mathrm{2}} −\mathrm{4}{a}+\mathrm{4}=\mathrm{4}{a}…