An Upper Bound

Algebra Level 5

Find the smallest integer \(N\) such that \[ \sqrt{x+1} + \sqrt{2x-3} + \sqrt{110-3x} \le N \] for all real numbers \(x\) in the common domain of the three square roots.

Details and assumptions

The common domain of the functions refers to the intersection of their domain, so that we are only dealing with real numbers.

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