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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