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New Zealand Contests
NZMOC Camp Selection Problems
2014 NZMOC Camp Selection Problems
1
1
Part of
2014 NZMOC Camp Selection Problems
Problems
(1)
(a + b)^3/ 4 >= a^2b + ab^2 for a,b>0
Source: New Zealand NZMOC Camp Selection Problems 2014 p1
9/19/2021
Prove that for all positive real numbers
a
a
a
and
b
b
b
:
(
a
+
b
)
3
4
≥
a
2
b
+
a
b
2
\frac{(a + b)^3}{4} \ge a^2b + ab^2
4
(
a
+
b
)
3
≥
a
2
b
+
a
b
2
algebra
inequalities