Let $\frac m n$ be an irreducible fraction such that $1 \gt \sqrt 2 + \sqrt 3 - \frac m n \gt 0$. Show that there is a constant $c \gt 0 \space$ such that $$\sqrt 2 + \sqrt 3 - \frac m n \gt \frac {1} {c \times n^4}$$ for every $n \gt 1.$
2026-04-01 00:28:40.1775003320
Inequality involving irreducible fractions and constants
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