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2021-IMOC
A7
A7
Part of
2021-IMOC
Problems
(1)
Another Inequality
Source: IMOC 2021 A7
8/11/2021
For any positive reals
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
that satisfy
a
2
+
b
2
+
c
2
+
d
2
=
4
,
a^2 + b^2 + c^2 + d^2 = 4,
a
2
+
b
2
+
c
2
+
d
2
=
4
,
show that
a
3
a
+
b
+
b
3
b
+
c
+
c
3
c
+
d
+
d
3
d
+
a
+
4
a
b
c
d
≤
6.
\frac{a^3}{a+b} + \frac{b^3}{b+c} + \frac{c^3}{c+d} + \frac{d^3}{d+a} + 4abcd \leq 6.
a
+
b
a
3
+
b
+
c
b
3
+
c
+
d
c
3
+
d
+
a
d
3
+
4
ab
c
d
≤
6.
algebra
Inequality
inequalities