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min/max of ((a+b+c)^2)/bc

Source: Bulgaria 1978 P4

June 17, 2021

inequalities

Problem Statement

Find the greatest possible real value of

S

and smallest possible value of

T

such that for every triangle with sides

a,b,c

(a\le b\le c)

to be true the inequalities:

S\le\frac{(a+b+c)^2}{bc}\le T.

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