Question Number 191552 by MATHEMATICSAM last updated on 25/Apr/23 $$\mathrm{If}\:{x}^{\mathrm{2}} \:−\:\mathrm{3}{x}\:+\:\mathrm{1}\:=\:\mathrm{0}\:\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\left({x}^{\mathrm{2}} \:+\:{x}\:+\:\frac{\mathrm{1}}{{x}}\:+\:\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right)^{\mathrm{2}} \\ $$ Answered by mr W last updated on 25/Apr/23…
Question Number 60475 by Tawa1 last updated on 21/May/19 Answered by tanmay last updated on 21/May/19 $$\frac{{dp}}{{dx}}=\frac{{f}\left({x}\right)\frac{{dg}\left({x}\right)}{{dx}}−\left[{g}\left({x}\right)−\mathrm{1}\right]\frac{{df}\left({x}\right)}{{dx}}}{\left\{{f}\left({x}\right)\right\}^{\mathrm{2}} } \\ $$$${p}'\left(\mathrm{2}\right)=\frac{{f}\left(\mathrm{2}\right){g}'\left(\mathrm{2}\right)−\left[{g}\left(\mathrm{2}\right)−\mathrm{1}\right]{f}'\left(\mathrm{2}\right)}{{f}^{\mathrm{2}} \left(\mathrm{2}\right)} \\ $$$$=\frac{\left(−\mathrm{1}\right)\left(−{sin}\mathrm{2}\right)−\left[{cos}\mathrm{2}−\mathrm{1}\right]\mathrm{5}}{\left(−\mathrm{1}\right)^{\mathrm{2}} } \\…
Question Number 191546 by MATHEMATICSAM last updated on 25/Apr/23 $$\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 $$\frac{\mathrm{1}}{\mathrm{2}}×\left\{\frac{\left({m}−\mathrm{2}\right)^{\mathrm{3}} }{\:\sqrt{{n}}}\:−{n}\right\}…
Question Number 191536 by MATHEMATICSAM last updated on 25/Apr/23 $$\mathrm{Factorize} \\ $$$$\frac{\mathrm{2}}{\mathrm{2}{x}\:−\:\mathrm{1}}\:−\mathrm{5}\:+\:\frac{\mathrm{3}}{\mathrm{3}{x}\:−\:\mathrm{1}} \\ $$ Answered by som(math1967) last updated on 25/Apr/23 $$\frac{\mathrm{2}}{\mathrm{2}{x}−\mathrm{1}}−\mathrm{3}+\frac{\mathrm{3}}{\mathrm{3}{x}−\mathrm{1}}−\mathrm{2} \\ $$$$=\frac{\mathrm{2}−\mathrm{6}{x}+\mathrm{3}}{\mathrm{2}{x}−\mathrm{1}}\:+\frac{\mathrm{3}−\mathrm{6}{x}+\mathrm{2}}{\mathrm{3}{x}−\mathrm{1}} \\…
Question Number 191529 by MATHEMATICSAM last updated on 25/Apr/23 $$\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 $$\frac{\left(\sqrt{{x}}−\sqrt{{y}}\right)\left(\sqrt{{x}}+\sqrt{{y}}\right)}{\:\sqrt{{xy}}\left(\sqrt{{x}}+\sqrt{{y}}\right)}=\frac{\mathrm{1}}{\:\sqrt{{x}}} \\ $$$${x}−\sqrt{{xy}}=\sqrt{{xy}}\Rightarrow{x}=\mathrm{2}\sqrt{{xy}}\Rightarrow\frac{{x}}{{y}}=\mathrm{4}\:\checkmark \\…
Question Number 191530 by Shrinava last updated on 25/Apr/23 Commented by mr W last updated on 25/Apr/23 $${question}\:{is}\:{wrong}.\:{figure}\:{is}\:{not} \\ $$$${possible}.\:{y}=\mathrm{0}. \\ $$ Commented by Shrinava…
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 $$\sqrt{\mathrm{3}}<\mathrm{2}<\sqrt{\mathrm{8}} \\ $$$${assume}\:{they}\:{are}\:{terms}\:{of}\:{an}\:{A}.{P}., \\ $$$${then}\:{we}\:{have}…
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Question Number 191527 by MATHEMATICSAM last updated on 25/Apr/23 $${x}\:+\:{y}\:=\:\mathrm{1}\:\mathrm{and}\:{x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:=\:\mathrm{2}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value} \\ $$$$\mathrm{of}\:{x}^{\mathrm{11}} \:+\:{y}^{\mathrm{11}} . \\ $$ Answered by Rasheed.Sindhi last updated on 25/Apr/23…