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Omni-MATH / Let f₀=f₁=1 and f_(i+2)=f_(i+1)+f_(i) for all n≥0. Find all real solutions to the equation x²⁰¹⁰=f₂₀₀₉⋅x+f₂₀₀₈

Problem

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problem

Let f0=f1=1f_0=f_1=1 and fi+2=fi+1+fif_{i+2}=f_{i+1}+f_i for all n≥0n\ge 0. Find all real solutions to the equation x2010=f2009⋅x+f2008x^{2010}=f_{2009}\cdot x+f_{2008}
Plain-text mathematical notation (without MathML)
Let f₀=f₁=1 and f_(i+2)=f_(i+1)+f_(i) for all n≥0. Find all real solutions to the equation 
x²⁰¹⁰=f₂₀₀₉⋅x+f₂₀₀₈
Original LaTeX notation
Let $f_0=f_1=1$ and $f_{i+2}=f_{i+1}+f_i$ for all $n\ge 0$. Find all real solutions to the equation 
\[x^{2010}=f_{2009}\cdot x+f_{2008}\]

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Source and history

task_id
f5adbcfc-4b44-5b0b-aaaf-f45e2550851b
task_key
test--f5adbcfc-4b44-5b0b-aaaf-f45e2550851b
task_revision_id
1
config / split
/ test

Official source

initial import