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3
Cyclic ineq with triangle sides
Cyclic ineq with triangle sides
Source: Moldavian TST_1
March 6, 2006
inequalities
algebra
polynomial
inequalities proposed
Problem Statement
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be sides of the triangle. Prove that
a
2
(
b
c
−
1
)
+
b
2
(
c
a
−
1
)
+
c
2
(
a
b
−
1
)
≥
0.
a^2\left(\frac{b}{c}-1\right)+b^2\left(\frac{c}{a}-1\right)+c^2\left(\frac{a}{b}-1\right)\geq 0 .
a
2
(
c
b
−
1
)
+
b
2
(
a
c
−
1
)
+
c
2
(
b
a
−
1
)
≥
0.
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