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Problem
Problem
Let
α
=
max
x
∈
R
{
8
2
sin
3
x
⋅
4
4
cos
3
x
}
\alpha = \max_{x \in \mathbb{R}} \{8^{2\sin 3x} \cdot 4^{4\cos 3x}\}
α
=
max
x
∈
R
{
8
2
s
i
n
3
x
⋅
4
4
c
o
s
3
x
}
and
β
=
min
x
∈
R
{
8
2
sin
3
x
⋅
4
4
cos
3
x
}
\beta = \min_{x \in \mathbb{R}} \{8^{2\sin 3x} \cdot 4^{4\cos 3x}\}
β
=
min
x
∈
R
{
8
2
s
i
n
3
x
⋅
4
4
c
o
s
3
x
}
. If
8
x
2
+
b
x
+
c
=
0
8x^2 + bx + c = 0
8
x
2
+
b
x
+
c
=
0
is a quadratic equation whose roots are
α
1
/
5
\alpha^{1/5}
α
1/5
and
β
1
/
5
\beta^{1/5}
β
1/5
, then the value of
c
−
b
c - b
c
−
b
is equal to: (a) 42 (b) 47 (c) 43 (d) 50
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