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Mathematics
Mathematics
Problem
If
a
,
b
,
c
a, b, c
a
,
b
,
c
are the sides of
Δ
A
B
C
\Delta ABC
Δ
A
B
C
such that
3
2
a
2
−
2
⋅
3
a
2
+
b
2
+
c
2
+
3
2
b
2
+
2
c
2
=
0
3^{2a^2} - 2 \cdot 3^{a^2 + b^2 + c^2} + 3^{2b^2 + 2c^2} = 0
3
2
a
2
−
2
⋅
3
a
2
+
b
2
+
c
2
+
3
2
b
2
+
2
c
2
=
0
, then If sides of
Δ
P
Q
R
\Delta PQR
Δ
P
QR
are
a
,
b
sec
C
,
c
cosec
C
a, b \sec C, c \operatorname{cosec} C
a
,
b
sec
C
,
c
cosec
C
. Then, area of
Δ
P
Q
R
\Delta PQR
Δ
P
QR
is a.
3
4
a
2
\frac{\sqrt{3}}{4}a^2
4
3
a
2
b.
3
4
b
2
\frac{\sqrt{3}}{4}b^2
4
3
b
2
c.
3
4
c
2
\frac{\sqrt{3}}{4}c^2
4
3
c
2
d.
1
2
a
b
c
\frac{1}{2}abc
2
1
ab
c
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