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Home » \div 1211 = 1 \quad \textand 1211 is prime? - Veritas Home Health

\div 1211 = 1 \quad \textand 1211 is prime? - Veritas Home Health

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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Solution: Let $ a = rac{p + q}{p - q} $ and $ b = rac{p - q}{p + q}...
R = a + rac{1}{a} - 2.
Define $ f(a) = a + rac{1}{a} - 2 $ for $ a > 1 $. By AM-GM, $ a + r...
R = rac{(p+q)^2 + (p-q)^2}{(p-q)(p+q)} - 2 = rac{p^2 + 2pq + q^2 + p...
R = 2\left( rac{p^2 + q^2}{p^2 - q^2} - 1
ight) = 2\left( rac{2q^2}{p^2 - q^2}
ight) = rac{4q^2}{p^2 - q^2}.
As $ p o q^+ $, $ R o \infty $. As $ p \gg q $, $ R o 0 $. So $ R >...
rac{p+q}{p-q} + rac{p-q}{p+q} \geq 2 \Rightarrow R = \left( rac{p+q}...
ight) - 2 \geq 2 - 2 = 0,

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