<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] $$ 4x^2 -2x +10 = 2(x+1)^2-(x+1)+3+2(x-1)^2-(x-1)+3$$
which means $f(x)=2x^2-x+3$
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