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Problem
Problem
Let
f
(
x
)
=
x
4
+
a
x
3
+
3
x
2
+
b
x
+
1
f(x) = x^4 + ax^3 + 3x^2 + bx + 1
f
(
x
)
=
x
4
+
a
x
3
+
3
x
2
+
b
x
+
1
,
a
,
b
∈
R
a, b \in R
a
,
b
∈
R
. If
f
(
x
)
≥
0
,
∀
x
∈
R
f(x) \ge 0, \forall x \in R
f
(
x
)
≥
0
,
∀
x
∈
R
, then the maximum value of
a
2
+
b
2
a^2 + b^2
a
2
+
b
2
is equal to
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