Monthly Archives: February 2007

The Arithmetic vs Geometric Mean Trick

One classical trick is the following: Since [tex] (x -y)^2 \ge 0, [/tex] we have [tex] x^2 – 2 x y + y^2 \ge 0 \implies x^2 + 2 x y + y^2 \ge 4xy [/tex] Taking root we obtain … Continue reading

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Silly Riddle

What’s the difference between jumping down from the 2nd floor versus the 20th floor? Ans: Splat! Aaaaaaahhhhh! (2nd floor) Aaaaaaaahhhhh! Splat! (20th floor) What if you jump from the 10th floor? It all depends on how long you remain in … Continue reading

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