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2018 Turkey Junior National Olympiad
4
4
Part of
2018 Turkey Junior National Olympiad
Problems
(1)
İnequality for all x,y,z positive real numbers
Source: Turkey Junior Math Olympiad 2018 #4
1/8/2019
For all
x
,
y
,
z
x,y,z
x
,
y
,
z
positive real numbers, find the all
c
c
c
positive real numbers that providing
x
3
y
+
y
3
z
+
z
3
x
x
+
y
+
z
+
4
c
x
y
z
≥
2
c
+
2
\frac{x^3y+y^3z+z^3x}{x+y+z}+\frac{4c}{xyz}\ge2c+2
x
+
y
+
z
x
3
y
+
y
3
z
+
z
3
x
+
x
yz
4
c
≥
2
c
+
2
inequalities
algebra
algebraic inequality