MathDB
min, max of (x^2+y^2+z^2)(1/x^2+1/y^2+1/z^2) if (x + y + z) (1/x+1/y+1/z)=10

Source: 2015 Saudi Arabia IMO TST IV p3

July 24, 2020
inequalitiesalgebraminmax

Problem Statement

Let a,b,ca, b,c be positive real numbers satisfying the condition (x+y+z)(1x+1y+1z)=10(x + y + z) \left( \frac{1}{x} + \frac{1}{y} + \frac{1}{z}\right)= 10 Find the greatest value and the least value of T=(x2+y2+z2)(1x2+1y2+1z2)T = (x^2 + y^2 + z^2) \left(\frac{1}{x^2} + \frac{1}{y^2} + \frac{1}{z^2}\right) Trần Nam Dũng
Back to ProblemsView on AoPS