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Author: Tinku Tara

a-curve-C-passes-through-2-0-and-the-slope-at-x-y-as-x-1-2-y-3-x-1-Find-the-equation-of-the-curve-

Question Number 131689 by liberty last updated on 07/Feb/21 $$\:\mathrm{a}\:\mathrm{curve}\:\mathrm{C}\:\mathrm{passes}\:\mathrm{through}\:\left(\mathrm{2},\mathrm{0}\right) \\ $$$$\mathrm{and}\:\mathrm{the}\:\mathrm{slope}\:\mathrm{at}\:\left(\mathrm{x},\mathrm{y}\right)\:\mathrm{as}\:\frac{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} +\left(\mathrm{y}−\mathrm{3}\right)}{\mathrm{x}+\mathrm{1}} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{curve}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

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Question Number 619 by Cheenz last updated on 11/Feb/15 $$\sqrt{\mathrm{2}+\sqrt{\mathrm{3}}}\:+\:\sqrt{\mathrm{2}−\sqrt{\mathrm{3}}}\:=\:? \\ $$ Answered by 123456 last updated on 11/Feb/15 $${x}=\sqrt{\mathrm{2}+\sqrt{\mathrm{3}}}+\sqrt{\mathrm{2}−\sqrt{\mathrm{3}}} \\ $$$${x}^{\mathrm{2}} =\mathrm{2}+\sqrt{\mathrm{3}}+\mathrm{2}\sqrt{\mathrm{2}+\sqrt{\mathrm{3}}}\sqrt{\mathrm{2}−\sqrt{\mathrm{3}}}+\mathrm{2}−\sqrt{\mathrm{3}} \\ $$$${x}^{\mathrm{2}}…

Let-and-are-the-roots-of-the-equation-x-2-6x-2-0-If-a-n-n-n-for-n-1-then-the-value-of-a-10-2a-8-2a-9-

Question Number 131688 by liberty last updated on 07/Feb/21 $$\:\mathrm{Let}\:\alpha\:\mathrm{and}\:\beta\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\: \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{x}^{\mathrm{2}} −\mathrm{6x}−\mathrm{2}=\mathrm{0}. \\ $$$$\mathrm{If}\:{a}_{{n}} \:=\:\alpha^{{n}} −\beta^{{n}} \:\mathrm{for}\:{n}\:\geqslant\mathrm{1}\: \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\frac{{a}_{\mathrm{10}} −\mathrm{2}{a}_{\mathrm{8}} }{\mathrm{2}{a}_{\mathrm{9}} }\:? \\ $$…