Question and Answers Forum

All Questions      Topic List

Relation and Functions Questions

Previous in All Question      Next in All Question      

Previous in Relation and Functions      Next in Relation and Functions      

Question Number 94382 by frc2crc last updated on 18/May/20

$$a_{n+1}=\sqrt{k+\sqrt{a_n}}{a}_0=\sqrt{k}$$$$howdoyousolvefork?$$$$OnlyEquationpleasenovalue$$$$fork$$

Commented by prakash jain last updated on 18/May/20

$$\mathrm{I}\mathrm{dont}\mathrm{think}\mathrm{it}\mathrm{possible}\mathrm{to}\mathrm{solve}\mathrm{for}k.$$$$$$$$\mathrm{Every}\mathrm{value}\mathrm{of}k\mathrm{defines}\mathrm{a}\mathrm{new}$$$$\mathrm{sequence}.$$$$$$$$\mathrm{For}\mathrm{example}$$$$a_{n+1}=\sqrt{1+\sqrt{1}}{a}_0=1\mathrm{is}\mathrm{one}\mathrm{sequence}$$$$a_{n+1}=\sqrt{2+\sqrt{2}}{a}_0=2\mathrm{is}\mathrm{another}\mathrm{sequence}$$$$\mathrm{You}\mathrm{need}\mathrm{to}\mathrm{have}\mathrm{at}\mathrm{least}\mathrm{one}$$$$\mathrm{more}\mathrm{constraint}\mathrm{on}{a}_n\mathrm{to}\mathrm{be}\mathrm{able}$$$$\mathrm{to}\mathrm{solve}\mathrm{for}k.$$

Commented by mr W last updated on 18/May/20

$$kcanbeanypositivevalue.whatdo$$$$youmeanwith‘‘solvefor{k}^{″}?$$

Answered by mathmax by abdo last updated on 20/May/20

$${\mathrm{a}}_{\mathrm{n}+1}=\mathrm{f}\left({\mathrm{a}}_{\mathrm{n}}\right)\mathrm{with}\mathrm{f}\left(\mathrm{x}\right)=\sqrt{\mathrm{k}+\sqrt{\mathrm{x}}}\mathrm{f}\mathrm{is}\mathrm{defined}\mathrm{on}[0,+\mathrm{\infty }[\mathrm{and}\mathrm{continue}$$$$\mathrm{the}\mathrm{limit}\mathrm{is}\mathrm{tbe}\mathrm{fixe}\mathrm{point}\mathrm{of}\mathrm{f}\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}\Rightarrow \mathrm{x}=\sqrt{\mathrm{k}+\sqrt{\mathrm{x}}}\Rightarrow$$$${\mathrm{x}}^2=\mathrm{k}+\sqrt{\mathrm{x}}\Rightarrow {\mathrm{x}}^2-\mathrm{k}=\sqrt{\mathrm{x}}\Rightarrow {({\mathrm{x}}^2-\mathrm{k})}^2=\mathrm{x}\Rightarrow {\mathrm{x}}^4-{2\mathrm{kx}}^2+{\mathrm{k}}^2-\mathrm{x}=0\Rightarrow$$$${\mathrm{x}}^4-{2\mathrm{kx}}^2-\mathrm{x}+\mathrm{k}=0\mathrm{rest}\mathrm{to}\mathrm{solve}\mathrm{this}\mathrm{equation}...\mathrm{be}\mathrm{continued}...$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com