mathmath333
  • mathmath333
Functions
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
what about them?
anonymous
  • anonymous
@Preetha
mathmath333
  • mathmath333
\(\large \color{black}{\begin{align} & f(x)=f(x-2)-f(x-1),\ x\in \mathbb{N} \hspace{.33em}\\~\\ & f(1)=0,f(2)=1 \hspace{.33em}\\~\\ & f(10)=? \hspace{.33em}\\~\\ \end{align}}\)

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mathmath333
  • mathmath333
i m looking for a short way
amoodarya
  • amoodarya
x∈N so f(x)∈N you can see f(x) as \[a_n\] so now \[a_{n}=a_{n-2}-a_{n-1}\\a_2=1\\a_1=0\\\] charachteristic equation \[t^2=1-t\\t^2+t-1=0\\a_n=A t_1^n +B t_2^n\]
amoodarya
  • amoodarya
find roots and apply initial condition you will have the closed formula for it
mathmath333
  • mathmath333
i didnt understand how u found this \(t^2=1-t\)
mathmath333
  • mathmath333
nor i have studied characteristic equation
amoodarya
  • amoodarya
oh ... i can't help you ,for fast method sorry

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