1) a + b + c = 0 Prove that 1/(2a ^ 2 + bc) + 1/(2b ^ 2 + ca) + 1/(2c ^ 2 + ab)
Answers
Answered by
0
Step-by-step explanation:
In the given Expression (Exp.), we have
3
variables
.
We try to reduce the no. of variables from
3
to
2
by using the given condition that
a
+
b
+
c
=
0
.
a
+
b
+
c
=
0
⇒
c
=
−
a
−
b
.
∴
2
a
2
+
b
c
=
2
a
2
+
b
(
−
a
−
b
)
=
2
a
2
−
a
b
−
b
2
,
=
(
a
−
b
)
(
2
a
+
b
)
.
Similarly,
2
b
2
+
c
a
=
2
b
2
+
a
(
−
a
−
b
)
=
2
b
2
−
a
b
−
a
2
,
=
(
b
−
a
)
(
2
b
+
a
)
.
Finally,
2
c
2
+
a
b
=
2
(
−
a
−
b
)
2
+
a
b
=
2
a
2
+
5
a
b
+
2
b
2
,
=
(
a
+
2
b
)
(
2
a
+
b
)
.
For ease of writing, let,
(
a
−
b
)
=
x
,
2
a
+
b
=
y
,
and
2
b
+
a
=
z
.
∴
The Exp.=
1
x
y
+
1
(
−
x
)
z
+
1
y
z
,
=
z
−
y
+
x
x
y
z
,
=
(
2
b
+
a
)
−
(
2
a
+
b
)
+
(
a
−
b
)
x
y
z
.
⇒
The Exp.=
0
,
as desired!
Similar questions
Physics,
3 hours ago
World Languages,
3 hours ago
English,
5 hours ago
Geography,
5 hours ago
Math,
8 months ago