MathDB

2

Part of 2018 India Regional Mathematical Olympiad

Problems(2)

Powers in Sum

Source: RMO 2018 P2

10/7/2018
Let nn be a natural number. Find all real numbers xx satisfying the equation ∑k=1nkxk1+x2k=n(n+1)4.\sum^n_{k=1}\frac{kx^k}{1+x^{2k}}=\frac{n(n+1)}4.
algebra
Polynomial in GP

Source: RMO 2018 P2

10/28/2018
Find the set of all real values of aa for which the real polynomial equation P(x)=x2−2ax+b=0P(x)=x^2-2ax+b=0 has real roots, given that P(0)⋅P(1)⋅P(2)≠0P(0)\cdot P(1)\cdot P(2)\neq 0 and P(0),P(1),P(2)P(0),P(1),P(2) form a geometric progression.
algebrapolynomial