Category: Algebra

Question Number 191546 by MATHEMATICSAM last updated on 25/Apr/23 $$\mathrm{If}\:{m}\:+\:\mathrm{1}\:=\:\sqrt{{n}}\:+\:\mathrm{3}\:\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{{m}^{\mathrm{3}} \:−\:\mathrm{6}{m}^{\mathrm{2}} \:+\:\mathrm{12}{m}\:−\mathrm{8}}{\:\sqrt{{n}}}\:−\:{n}\right) \\ $$ Answered by som(math1967) last updated on 25/Apr/23 $$\frac{\mathrm{1}}{\mathrm{2}}×\left\{\frac{\left({m}−\mathrm{2}\right)^{\mathrm{3}} }{\:\sqrt{{n}}}\:−{n}\right\}…

Question Number 191529 by MATHEMATICSAM last updated on 25/Apr/23 $$\mathrm{If}\:\frac{{x}\:−\:{y}}{{x}\sqrt{{y}}\:+\:{y}\sqrt{{x}}}\:=\:\frac{\mathrm{1}}{\:\sqrt{{x}}}\:;\:\left({x}\:>\:\mathrm{0}\:\mathrm{and}\:{y}\:>\:\mathrm{0}\right)\:\mathrm{then} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\frac{{x}}{{y}}\:. \\ $$ Answered by mehdee42 last updated on 25/Apr/23 $$\frac{\left(\sqrt{{x}}−\sqrt{{y}}\right)\left(\sqrt{{x}}+\sqrt{{y}}\right)}{\:\sqrt{{xy}}\left(\sqrt{{x}}+\sqrt{{y}}\right)}=\frac{\mathrm{1}}{\:\sqrt{{x}}} \\ $$$${x}−\sqrt{{xy}}=\sqrt{{xy}}\Rightarrow{x}=\mathrm{2}\sqrt{{xy}}\Rightarrow\frac{{x}}{{y}}=\mathrm{4}\:\checkmark \\…

Question Number 191525 by mehdee42 last updated on 25/Apr/23 $${Q}\::\:{Show}\:{that}\:{the}\:{numbers}\:\sqrt{\mathrm{3}\:}\:,\:\mathrm{2}\:\&\:\sqrt{\mathrm{8}}\:{cannot}\:{be}\:{terms}\:{of}\:{an}\:{arithmetic}\:{sequence}. \\ $$ Answered by mr W last updated on 26/Apr/23 $$\sqrt{\mathrm{3}}<\mathrm{2}<\sqrt{\mathrm{8}} \\ $$$${assume}\:{they}\:{are}\:{terms}\:{of}\:{an}\:{A}.{P}., \\ $$$${then}\:{we}\:{have}…

Question Number 60453 by Tawa1 last updated on 21/May/19 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 60445 by ANTARES VY last updated on 21/May/19 Commented by bhanukumarb2@gmail.com last updated on 21/May/19 $${cauchy}\:{inequality}\: \\ $$ Answered by MJS last updated…