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UPSC CDS Basic operation and Factorisation Questions
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© examsnet.com
Question : 2
Total: 77
What is the value of
(
x
−
y
)
3
+
(
y
−
z
)
3
+
(
z
−
x
)
3
9
(
x
−
y
)
(
y
−
z
)
(
z
−
x
)
[2019 CDS-II]
0
1
3
1
9
1
Validate
Solution:
We know if
a
+
b
+
c
=
0
then
a
3
+
b
3
+
c
3
=
3
a
b
c
Here
(
x
−
y
)
+
(
y
−
z
)
+
(
z
−
x
)
=
0
⇒
(
x
−
y
)
3
(
y
−
z
)
3
+
(
z
−
x
)
3
=
3
(
x
−
y
)
(
y
−
z
)
(
z
−
x
)
∴
(
x
−
y
)
3
+
(
y
−
z
)
3
+
(
z
−
x
)
3
9
(
x
−
y
)
(
y
−
z
)
(
z
−
x
)
=
3
(
x
−
y
)
(
y
−
z
)
(
z
−
x
)
9
(
x
−
y
)
(
y
−
z
)
(
z
−
x
)
=
1
3
© examsnet.com
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