1
Part of 2002 Vietnam National Olympiad
Problems(2)
Vietnam NMO 2002_1
Source:
10/26/2008
Solve the equation \sqrt{4 \minus{} 3\sqrt{10 \minus{} 3x}} \equal{} x \minus{} 2.
complex numbersalgebra proposedalgebra
Vietnam NMO 2002_4
Source:
10/26/2008
Let , , be real numbers for which the polynomial x^3 \plus{} ax^2 \plus{} bx \plus{} c has three real roots. Prove that 12ab \plus{} 27c \le 6a^3 \plus{} 10\left(a^2 \minus{} 2b\right)^{\frac {3}{2}} When does equality occur?
algebrapolynomialinequalities unsolvedinequalities