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Dutch IMO TST
2016 Dutch IMO TST
1
a +\sqrt{ab}+ \sqrt[3]{abc} <= 4/3 (a + b + c)
a +\sqrt{ab}+ \sqrt[3]{abc} <= 4/3 (a + b + c)
Source: Dutch IMO TST 2016 day 2 p1
August 30, 2019
algebra
inequalities
Problem Statement
Prove that for all positive reals
a
,
b
,
c
a, b,c
a
,
b
,
c
we have:
a
+
a
b
+
a
b
c
3
≤
4
3
(
a
+
b
+
c
)
a +\sqrt{ab}+ \sqrt[3]{abc}\le \frac43 (a + b + c)
a
+
ab
+
3
ab
c
≤
3
4
(
a
+
b
+
c
)
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