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Mathematics
Problem
Which of the following inequalities holds for all non-negative real numbers
a
a
a
and
b
b
b
? a)
(
a
+
b
)
2
≤
4
a
b
(a+b)^2\le4ab
(
a
+
b
)
2
≤
4
ab
b)
a
+
b
2
≥
a
b
\dfrac{a+b}{2}\ge\sqrt{ab}
2
a
+
b
≥
ab
c)
a
+
b
≥
2
a
b
a+b\ge2ab
a
+
b
≥
2
ab
d)
a
+
b
2
≤
a
b
\dfrac{a+b}{2}\le\sqrt{ab}
2
a
+
b
≤
ab
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