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Category: Algebra

If-are-the-real-roots-of-the-equation-a-3-6a-2-3a-1-0-then-find-all-possible-values-of-the-expression-2-2-2-

Question Number 124056 by Snail last updated on 30/Nov/20 $${If}\:\alpha,\beta,\gamma\:{are}\:{the}\:{real}\:{roots}\:{of}\:{the}\:{equation}\: \\ $$$${a}^{\mathrm{3}} −\mathrm{6}{a}^{\mathrm{2}} +\mathrm{3}{a}+\mathrm{1}=\mathrm{0}\:\:\:\:\:{then}\:{find}\:{all}\:{possible}\:{values} \\ $$$${of}\:{the}?{expression}\:\alpha^{\mathrm{2}} \beta+\beta^{\mathrm{2}} \gamma+\gamma^{\mathrm{2}} \alpha \\ $$ Commented by MJS_new last…

2-x-2-x-4-x-1-2-x-

Question Number 189576 by normans last updated on 18/Mar/23 $$ \\ $$$$\:\:\:\:\:\mathrm{2}^{\boldsymbol{{x}}} \:+\:\mathrm{2}^{\boldsymbol{{x}}} −\mathrm{4}\:+\:\boldsymbol{{x}}\:=\:−\frac{\mathrm{1}}{\mathrm{2}}\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\boldsymbol{{x}}\:=\:??? \\ $$$$ \\ $$ Answered by Gbenga last updated…

The-number-of-pairs-of-natural-numbers-x-y-satisfy-x-2-y-gcd-x-y-2-2023-

Question Number 189531 by cortano12 last updated on 18/Mar/23 $$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{pairs}\:\mathrm{of}\:\mathrm{natural} \\ $$$$\mathrm{numbers}\:\left(\mathrm{x},\mathrm{y}\right)\:\mathrm{satisfy} \\ $$$$\:\:\:\:\:\:\mathrm{x}^{\mathrm{2}} \mathrm{y}+\mathrm{gcd}\left(\mathrm{x},\mathrm{y}^{\mathrm{2}} \right)=\mathrm{2023} \\ $$ Answered by aleks041103 last updated on 19/Mar/23…