Talk:Analytic Maths for Olympiads

Welcome to the Brainstorm Forum for Olympiad Algebra and Induction

Part of the School of Olympiads

POST YOUR QUESTIONS ON THIS TALKPAGE AND GET ANSWERS FROM OTHER VIEWERS. ALSO WE CAN DISCUSS SOLUTIONS AND DISAGREEMENTS.

For more Resources visit Analytic Maths for Olympiads

A picking game (problem on induction)

There is a heap of $n$ matches. 2 players take turns to pick 1 or 2 matches. The winner is the person who picks the last match.

• Who wins for 5 matches (if no player misses a chance to win or draw)?
• Is there a general strategy for any number of matches (to force a win or a tie for either side)?
• What is the strategy if existing?

A Rootful Question

Prove the following:

• $5<\sqrt{5}+\sqrt[3]{5}+\sqrt[4]{5}$
• $8>\sqrt{8}+\sqrt[3]{8}+\sqrt[4]{8}$
• $9>\sqrt{n}+\sqrt[3]{n}+\sqrt[4]{n},n\geq 9$

A problem on functions

Find all pairs of real numbers (a,b) such that: f(x)= x² + ax + b If q is a root of f(x) then q²-2 is also a root