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Category: Algebra

Find-the-condition-that-one-root-of-ax-2-bx-c-0-a-0-is-square-of-the-other-

Question Number 132697 by liberty last updated on 15/Feb/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{condition}\:\mathrm{that}\:\mathrm{one} \\ $$$$\mathrm{root}\:\mathrm{of}\:{ax}^{\mathrm{2}} +{bx}+{c}\:=\:\mathrm{0}\:,{a}\neq\:\mathrm{0} \\ $$$$\mathrm{is}\:\mathrm{square}\:\mathrm{of}\:\mathrm{the}\:\mathrm{other}\:. \\ $$ Commented by liberty last updated on 16/Feb/21 $$\mathrm{okay}…

factorize-2x-3-1-

Question Number 67136 by ,jamiebots last updated on 23/Aug/19 $${factorize}\:\mathrm{2}{x}^{\mathrm{3}} −\mathrm{1} \\ $$ Answered by Cmr 237 last updated on 23/Aug/19 $$\mathrm{2x}^{\mathrm{3}} −\mathrm{1}=\mathrm{2}\left(\mathrm{x}^{\mathrm{3}} −\frac{\mathrm{1}}{\mathrm{2}}\right)=\mathrm{p}\left(\mathrm{x}\right) \\…

Let-is-cube-root-of-unity-and-x-y-z-Z-If-x-y-z-0-prove-that-3-x-y-z-Show-by-an-example-that-the-converse-is-not-true-

Question Number 1585 by Rasheed Soomro last updated on 22/Aug/15 $$\mathrm{Let}\:\omega\:\mathrm{is}\:\mathrm{cube}\:\mathrm{root}\:\mathrm{of}\:\mathrm{unity}\:\mathrm{and}\:\mathrm{x},\mathrm{y},\mathrm{z}\:\in\:\mathbb{Z} \\ $$$$\mathrm{If}\:\omega^{\mathrm{x}} +\omega^{\mathrm{y}} +\omega^{\mathrm{z}} =\mathrm{0}\:\mathrm{prove}\:\mathrm{that}\:\mathrm{3}\:\mid\:\left(\mathrm{x}+\mathrm{y}+\mathrm{z}\right) \\ $$$$\mathrm{Show}\:{by}\:{an}\:{example}\:\mathrm{that}\:\mathrm{the}\:\mathrm{converse}\:\mathrm{is}\:{not}\:\:\mathrm{true}. \\ $$ Commented by 112358 last updated…

Determine-three-complex-numbers-such-that-2-but-2-2-but-2-2-but-2-

Question Number 1540 by Rasheed Soomro last updated on 17/Aug/15 $$\mathrm{Determine}\:\mathrm{three}\:\mathrm{complex}\:\mathrm{numbers}\:\alpha\:,\:\beta\:,\gamma\:\:\mathrm{such}\:\mathrm{that} \\ $$$$\alpha=\beta^{\:\mathrm{2}} \:\:\:\:\:\:\:{but}\:\:\:\:\beta\:\neq\:\alpha^{\:\mathrm{2}} \\ $$$$\beta\:=\:\gamma^{\:\mathrm{2}} \:\:\:\:\:\:{but}\:\:\:\:\:\gamma\:\neq\:\beta^{\:\mathrm{2}} \\ $$$$\gamma\:=\:\alpha^{\:\mathrm{2}\:} \:\:\:\:\:{but}\:\:\:\:\:\alpha\:\neq\:\gamma^{\:\mathrm{2}} \\ $$ Answered by 123456…

Find-complex-numbers-and-such-that-m-n-and-m-n-m-n-Z-Determine-formula-for-the-number-of-pairs-fulfilling-the-above-conditions-You-may-ignore-this-part

Question Number 1498 by Rasheed Soomro last updated on 14/Aug/15 $$\mathrm{Find}\:\mathrm{complex}\:\mathrm{numbers}\:\alpha\:{and}\:\:\beta\:\:\mathrm{such}\:\mathrm{that} \\ $$$$\alpha^{\:{m}} =\beta^{\:\:{n}} \:\:\:\:{and}\:\:\:\beta^{\:\:{m}} =\alpha^{\mathrm{n}} \:\:,\:{m},{n}\:\in\:\mathbb{Z} \\ $$$$\boldsymbol{\mathrm{D}}\mathrm{etermine}\:\mathrm{formula}\:\mathrm{for}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{pairs}\:\left(\alpha,\beta\right)\:\mathrm{fulfilling}\:\mathrm{the} \\ $$$$\mathrm{above}\:\mathrm{conditions}.\:\:\left(\:\mathrm{You}\:\mathrm{may}\:\mathrm{ignore}\:\mathrm{this}\:\mathrm{part}\:\mathrm{in}\:\mathrm{your}\:\mathrm{answer}\right) \\ $$ Commented by…

Question-67025

Question Number 67025 by Masumsiddiqui399@gmail.com last updated on 21/Aug/19 Commented by Rasheed.Sindhi last updated on 22/Aug/19 $${x}^{{x}^{{x}+\mathrm{5}} } =\:^{\mathrm{3}} \sqrt{\mathrm{3}} \\ $$$$\left({x}^{{x}^{{x}+\mathrm{5}} } \right)^{\mathrm{3}} =\left(\:^{\mathrm{3}}…

Prove-that-a-b-c-d-a-c-d-b-

Question Number 1483 by Rasheed Ahmad last updated on 13/Aug/15 $$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{a}+\left(\mathrm{b}+\mathrm{c}\right)+\mathrm{d}=\left(\mathrm{a}+\mathrm{c}\right)+\left(\mathrm{d}+\mathrm{b}\right) \\ $$ Commented by prakash jain last updated on 13/Aug/15 $$\mathrm{Basic}\:\mathrm{properties}\:\mathrm{of}\:+\:\mathrm{operator}.\:\mathrm{Or}\:\mathrm{is}\:\mathrm{it} \\…