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5
Inequality involving square roots
Inequality involving square roots
Source:
December 31, 2011
inequalities
inequalities unsolved
Problem Statement
Let
a
,
b
a, b
a
,
b
and
c
c
c
be positive real numbers. Prove that
a
2
+
b
c
b
+
c
+
b
2
+
c
a
c
+
a
+
c
2
+
a
b
a
+
b
≥
a
b
+
c
+
b
c
+
a
+
c
a
+
b
\frac{\sqrt{a^2+bc}}{b+c}+\frac{\sqrt{b^2+ca}}{c+a}+\frac{\sqrt{c^2+ab}}{a+b}\ge\sqrt{\frac{a}{b+c}}+\sqrt{\frac{b}{c+a}}+\sqrt{\frac{c}{a+b}}
b
+
c
a
2
+
b
c
+
c
+
a
b
2
+
c
a
+
a
+
b
c
2
+
ab
≥
b
+
c
a
+
c
+
a
b
+
a
+
b
c
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