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1/(1+a)+1/(1+b)+1/(1+c)+1/(1+d)> t, max t wanted

Source: 1987 Swedish Mathematical Competition p5

March 28, 2021

algebrainequalities

Problem Statement

Show that there exists a positive number t such that for all positive numbers

a,b,c,d

with

abcd = 1

\frac{1}{1+a}+\frac{1}{1+b}+\frac{1}{1+c}+\frac{1}{1+d}> t.

and find the largest

t

with this property.