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Mathematics
Mathematics
Problem
The minimum value of
(
A
2
+
A
+
1
)
(
B
2
+
B
+
1
)
(
C
2
+
C
+
1
)
(
D
2
+
D
+
1
)
A
B
C
D
\frac{(A^2 + A + 1)(B^2 + B + 1)(C^2 + C + 1)(D^2 + D + 1)}{ABCD}
A
B
C
D
(
A
2
+
A
+
1
)
(
B
2
+
B
+
1
)
(
C
2
+
C
+
1
)
(
D
2
+
D
+
1
)
where
A
,
B
,
C
,
D
>
0
A, B, C, D > 0
A
,
B
,
C
,
D
>
0
is : (a)
1
3
4
\frac{1}{3^4}
3
4
1
(b)
1
2
4
\frac{1}{2^4}
2
4
1
(c)
2
4
2^4
2
4
(d)
3
4
3^4
3
4
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