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Olympiad
Hard
Inequalities
10–12
For
x
>
0
x > 0
x
>
0
, what is the minimum value of
x
2
+
16
x
x^{2} + \frac{16}{x}
x
2
+
x
16
?
Para
x
>
0
x > 0
x
>
0
, qual é o valor mínimo de
x
2
+
16
x
x^{2} + \frac{16}{x}
x
2
+
x
16
?
Answer options
A.
8
2
8\sqrt{2}
8
2
B.
16
C.
12
D.
8
Check Answer
Solution
Step 1 of 3
1.
Split the second term in two:
x
2
+
8
x
+
8
x
x^{2} + \frac{8}{x} + \frac{8}{x}
x
2
+
x
8
+
x
8
.
Next step
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