Let $r$, $s$, and $t$ be the roots of the equation $x^3 - 2x + 1 = 0$ in some order. What is the maximal value of $r^3 - s- t$?
How should I approach this problem? I have no idea how to start, any answer is greatly appreciated.
2026-04-03 20:18:33.1775247513
Let $r$, $s$, and $t$ be the roots of the equation $x^3 - 2x + 1 = 0$ in some order. What is the maximal value of $r^3 - s- t$?
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for any or the three roots.
$r^3 - 2r + 1 = 0\\ r^3 = 2r - 1$
substitute: $2r - s - t - 1$
$r + s + t = 0$ from Vieta.
Substitute again
$3r - 1$
What is the largest of the 3 roots?