# New insight to problem 3, IMO 1973

Algebra Level 5

$\large x^4+ax^3+bx^2+ax+1=0$$$A$$ is a set of points $$(a, b)$$ at which the equation above has at least one real root. If $$b=f(a)$$ is the expression of boundary of set $$A$$, find the value of $$f(7)+f\left( \frac{19}{8} \right)$$.

Details and Assumptions:

• $$a$$, $$b$$ are real numbers.
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