MathDB
IOQM 2022-23 P-15

Source:

October 30, 2022
algebrainequalitiesIOQM

Problem Statement

Let x,yx,y be real numbers such that xy=1xy=1. Let TT and tt be the largest and smallest values of the expression \\ (x+y)2−(x−y)−2(x+y)2+(x−y)−2\hspace{2cm} \frac{(x+y)^2-(x-y)-2}{(x+y)^2+(x-y)-2}\\. \\ If T+tT+t can be expressed in the form mn\frac{m}{n} where m,nm,n are nonzero integers with GCD(m,n)=1GCD(m,n)=1, find the value of m+nm+n.
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