Difference between revisions of "2015 Final tour - Azerbaijan in lower age category"

Revision as of 02:28, 27 June 2015

1) a, b, and c are positive real numbers that abc=1/8. Prove a^2+b^2+c^2+a^2*b^2+a^2*c^2+b^2*c^2>=15/16 (2 points)

2) a, b and c are sides of triangle. Prove that area of triangle isn't more than (a^2+b^2+c^2)/6.

3) Find all P(x) polynomials that has real coefficient, which for all real numbers of x this equation must be true: P(P(x))=(x^2+x+1)*P(x)

4) Natural nu

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 ) a, b and c are sides of triangle. Prove that area of triangle isn't more than (a^2+b^2+c^2)/6.
+) Find all P(x) polynomials that has real coefficient, which for all real numbers of x this equation must be true:
+P(P(x))=(x^2+x+1)*P(x)
+) Natural nu