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Mathematics
Mathematics
Problem
Let
a
,
b
>
0
a, b > 0
a
,
b
>
0
and
α
=
i
^
a
+
4
j
^
b
+
b
k
^
\alpha = \frac{\hat{i}}{a} + \frac{4\hat{j}}{b} + b\hat{k}
α
=
a
i
^
+
b
4
j
^
+
b
k
^
and
β
=
b
i
^
+
a
j
^
+
1
b
k
^
\beta = b\hat{i} + a\hat{j} + \frac{1}{b}\hat{k}
β
=
b
i
^
+
a
j
^
+
b
1
k
^
, then the maximum value of
10
5
+
α
⋅
β
\frac{10}{5 + \alpha \cdot \beta}
5
+
α
⋅
β
10
is a. 1 b. 2 c. 4 d. 8
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