If pqr =1 ,then find the value of
(1/1+p+q^-1)+(1/1+q+r^-1)+
(1/1+r+p^-1).
please solve it quickly...
Answers
Explanation:
@Nimo N wrote an answer:
"Expect to use a lot of paper and pencil lead, possibly causing significant wear on an eraser, as well............"
So,I tried this question ,see below.
Preparation of mind before answer :
Let ,
x
=
1
1
+
p
+
q
−
1
,
y
=
1
1
+
q
+
r
−
1
,
and
z
=
1
1
+
r
+
p
−
1
Now,
x
=
1
1
+
p
+
(
1
q
)
=
q
q
+
p
q
+
1
=
q
(
p
q
+
q
+
1
)
Here denominator of x is
(
p
q
+
q
+
1
)
.
We obtain same denominator for y and z.
To do so, we have to put value of
r
from
p
q
r
=
1
.
i
.
e
.
r
=
1
p
q
or
1
r
=
p
q
So,
y
=
1
1
+
q
+
(
1
r
)
=
1
1
+
q
+
p
q
=
1
(
p
q
+
q
+
1
)
and
z
=
1
1
+
r
+
1
p
=
1
1
+
1
p
q
+
1
p
=
p
q
p
q
+
1
+
q
=
p
q
(
p
q
+
q
+
1
)
We can see that denominators of x,y and z are same
:
i
.
e
.
(
p
q
+
q
+
1
)
Now ,it is easy to solve problem . Please see the solution.
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
.
.
ANSWER :
We have,
p
q
r
=
1
⇒
r
=
1
p
q
or
1
r
=
p
q
L
H
S
=
1
1
+
p
+
q
−
1
+
1
1
+
q
+
r
−
1
+
1
1
+
r
+
p
−
1
L
H
S
=
1
1
+
p
+
(
1
q
)
+
1
1
+
q
+
(
1
r
)
+
1
1
+
r
+
1
p
L
H
S
=
q
q
+
p
q
+
1
+
1
1
+
q
+
p
q
+
1
1
+
1
p
q
+
1
p
L
H
S
=
q
(
p
q
+
q
+
1
)
+
1
(
p
q
+
q
+
1
)
+
p
q
(
p
q
+
q
+
1
)
L
H
S
=
q
+
1
+
p
q
(
p
q
+
q
+
1
)
L
H
S
=
p
q
+
q
+
1
(
p
q
+
q
+
1
)
L
H
S
=
1
L
H
S
=
R
H
S
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
.
.
Practice :Try yourself to obtain same denominator of x,y and z :
(
i
)
(
q
r
+
r
+
1
)
and
(
i
i
)
(
p
r
+
p
+
1
)