<s>[INST] If $f(x+1)+f(x-1)=4x^2-2x+10$ then what is $f(x)$ 
If $$f(x+1) +f(x-1)= 4x^2 -2x +10$$  then what is $f(x)$ 

What is strategy of solving this kind of  problems ?
Thank you for help
 [/INST] *

*Find one solution


Try to find it as $f_0(x) = ax^2 +bx + c$
$f_0(x+1) + f_0(x-1) = 2ax^2 + 2a + 2bx +2c$ => $f_0(x)=2x^2-x + 3$


*$f(x) = f_0(x) + g(x)$ => $g(x-1) + g(x+1) =0$


Find all $g(x)$
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