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Byju's Answer
Standard XII
Mathematics
Sum of n Terms
p, q and r ar...
Question
p, q and r are in AP, then prove that (p + 2q - r) (2q + r -p) (r + p - q) = 4pqr.
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Solution
Given
p
,
q
,
r
are in
A
P
∴
q
−
p
=
r
−
q
(distance between
p
&
q
is equal to distance between
q
&
r
)
∴
2
q
=
r
+
p
.
.
.
.
.
.
(
1
)
L
H
S
=
(
p
+
2
q
−
r
)
(
2
q
+
r
−
p
)
(
r
+
p
−
q
)
=
(
p
+
r
+
p
−
r
)
(
r
+
p
+
r
−
p
)
(
r
+
p
−
q
)
[
∵
from eqn
(
1
)
sub for
2
q
]
=
2
p
.2
r
(
2
q
−
q
)
(from eqn
(
1
)
)
=
4
p
q
r
=
R
H
S
Hence proved
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0
Similar questions
Q.
If
p
,
q
and
r
in
A
P
, then prove that
(
p
+
2
q
−
r
)
(
2
q
+
r
−
p
)
(
r
+
p
−
q
)
=
4
p
q
r
.
Q.
If
p
(
q
−
r
)
x
2
+
q
(
r
−
p
)
x
+
r
(
p
−
q
)
=
0
has equal roots, then
2
q
=
Q.
Let
→
p
,
→
q
,
→
r
be three unit vectors such that
→
p
×
→
q
=
→
r
. If
→
a
is any vector such that
[
→
a
→
q
→
r
]
=
1
,
[
→
a
→
r
→
p
]
=
2
and
[
→
a
→
p
→
q
]
=
3
then
→
a
is
Q.
Let
A
=
⎛
⎜
⎝
0
2
q
r
p
q
−
r
p
−
q
r
⎞
⎟
⎠
. If
A
A
T
=
I
3
, then
|
p
|
is:
Q.
Three numbers p, q and r are pairwise coprime. If the product of p and q is 629 and that of q and r is 391, then find the value of (p + 2q + r).
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