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Mathematics
Mathematics
Problem
If
a
,
b
,
c
a, b, c
a
,
b
,
c
and
A
,
B
,
C
∈
R
∖
{
0
}
A, B, C \in \mathbb{R} \setminus \{0\}
A
,
B
,
C
∈
R
∖
{
0
}
such that
a
A
+
b
B
+
c
C
+
(
a
2
+
b
2
+
c
2
)
(
A
2
+
B
2
+
C
2
)
=
0
,
then
aA + bB + cC + \sqrt{(a^2 + b^2 + c^2)(A^2 + B^2 + C^2)} = 0, \text{ then}
a
A
+
b
B
+
c
C
+
(
a
2
+
b
2
+
c
2
)
(
A
2
+
B
2
+
C
2
)
=
0
,
then
value of
a
B
b
A
+
b
C
c
B
+
c
A
a
C
\frac{aB}{bA} + \frac{bC}{cB} + \frac{cA}{aC}
b
A
a
B
+
c
B
b
C
+
a
C
c
A
is a. 3 b. 4 c. 5 d. 6
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