Compete · Slovenia
Odbirno tekmovanje (qualifying round) 2023
1Let \(x\) and \(y\) be real numbers satisfying \(y - x = 2\). Compute the value of the expression \[ 2x^3 + y^3 - 3y^2x + 6x^2 . \]2Find all integers \(n\) for which the number \[ \frac{9n+8}{n+7} \] is also an integer.
Work through the paper in order - each problem opens in the workspace with this paper as its trail.