MathDB

systems x+y=1 & (ax+by)^2<=a^2x+b^2y, x+y=1 & (ax+by)^4<=a^4x+b^4y

Source: Spanish Mathematical Olympiad 1987 P4

August 2, 2018

algebraSystem

Problem Statement

a

and

b

are distinct real numbers, solve the systems (a)

\begin{cases} x+y = 1 \\ (ax+by)^2 \le a^2x+b^2y \end{cases}

and (b)

\begin{cases} x+y = 1 \\ (ax+by)^4 \le a^4x+b^4y \end{cases}