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Author: Tinku Tara

Find-all-polynomials-P-x-with-real-coefficients-such-that-for-all-nonzero-real-numbers-x-P-x-P-1-x-P-x-1-x-P-x-1-x-2-

Question Number 200722 by cortano12 last updated on 22/Nov/23 $$\:\:\mathrm{Find}\:\mathrm{all}\:\mathrm{polynomials}\:\mathrm{P}\left(\mathrm{x}\right)\:\mathrm{with} \\ $$$$\:\mathrm{real}\:\mathrm{coefficients}\:\mathrm{such}\:\mathrm{that}\:\mathrm{for} \\ $$$$\:\mathrm{all}\:\mathrm{nonzero}\:\mathrm{real}\:\mathrm{numbers}\:\mathrm{x},\: \\ $$$$\:\:\:\:\:\mathrm{P}\left(\mathrm{x}\right)+\mathrm{P}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)=\frac{\mathrm{P}\left(\mathrm{x}+\frac{\mathrm{1}}{\mathrm{x}}\right)+\mathrm{P}\left(\mathrm{x}−\frac{\mathrm{1}}{\mathrm{x}}\right)}{\mathrm{2}}\:\:\: \\ $$ Commented by Frix last updated on 22/Nov/23…

1-a-8-b-5-6-a-b-max-

Question Number 200716 by hardmath last updated on 22/Nov/23 $$\mathrm{1}.\: \\ $$$$\frac{{a}}{\mathrm{8}}\:+\:\frac{{b}}{\mathrm{5}}\:=\:\mathrm{6}\:\:\:\Rightarrow\:\:\:\left({a}+{b}\right)_{\boldsymbol{{max}}} \:=\:? \\ $$ Answered by AST last updated on 22/Nov/23 $$\mathrm{5}{a}+\mathrm{8}{b}=\mathrm{240}\Rightarrow{a}=\frac{\mathrm{240}−\mathrm{8}{b}}{\mathrm{5}} \\ $$$${remains}\:{to}\:{find}\:\left({a}+{b}\right)_{{max}}…

3-1-3-5-7-2n-1-

Question Number 200718 by hardmath last updated on 22/Nov/23 $$\mathrm{3}. \\ $$$$\mathrm{1}+\mathrm{3}+\mathrm{5}+\mathrm{7}+…+\left(\mathrm{2}{n}+\mathrm{1}\right)\:=\:? \\ $$ Answered by AST last updated on 22/Nov/23 $$\mathrm{2}+\mathrm{4}+..+\mathrm{2}{n}=\mathrm{2}\left(\mathrm{1}+\mathrm{2}+\mathrm{3}+…+{n}\right)={n}^{\mathrm{2}} +{n} \\ $$$$\mathrm{1}+\mathrm{2}+\mathrm{3}+…+\mathrm{2}{n}+\mathrm{1}=\left(\mathrm{2}{n}+\mathrm{1}\right)\left({n}+\mathrm{1}\right)…

help-me-derived-the-formular-of-motion-

Question Number 200632 by pascal889 last updated on 21/Nov/23 $$\boldsymbol{\mathrm{help}}\:\boldsymbol{\mathrm{me}}\:\boldsymbol{\mathrm{derived}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{formular}}\:\boldsymbol{\mathrm{of}} \\ $$$$\:\boldsymbol{\mathrm{motion}} \\ $$ Commented by mr W last updated on 21/Nov/23 $${do}\:{you}\:{really}\:{think}\:{this}\:{is}\: \\ $$$${appropriate}?\:{this}\:{is}\:{like}\:{when}\:{i}\:{ask}…