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w =\frac{3b + 2c}{6a}+\frac{2c + 6a}{3b}+\frac{6a + 3b}{2c} if 1/a+2/b+3/c=0

Source: 2003 Bosnia & Herzegovina JBMO TST p1

May 27, 2020

algebra

Problem Statement

Non-zero real numbers

a, b, c

satisfy the condition

\frac{1}{a}+\frac{2}{b}+\frac{3}{c}= 0

.
Determine the value of

w =\frac{3b + 2c}{6a}+\frac{2c + 6a}{3b}+\frac{6a + 3b}{2c}