MathDB
Max and Min

Source: 1993 National High School Mathematics League, Exam One, Problem 8

February 27, 2020

Problem Statement

Real number x,yx,y satisfy that 4x2−5xy+4y2=5,S=x2+y24x^2-5xy+4y^2=5,S=x^2+y^2, then 1Smax+1Smin=\frac{1}{S_\text{max}}+\frac{1}{S_\text{min}}=________.
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