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AFCAT Model Paper 10
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© examsnet.com
Question : 51
Total: 100
What is the value of the expression?
(
a
−
b
)
3
+
(
b
−
c
)
3
+
(
c
−
a
)
3
3
(
a
−
b
)
(
b
−
c
)
(
c
−
a
)
=
?
4
1
2
0
Validate
Solution:
Formula Used:
x
3
+
y
3
+
z
3
−
3
x
y
z
=
(
x
+
y
+
z
)
(
x
2
+
y
2
+
z
2
−
x
y
−
y
z
−
z
x
)
x
3
+
y
3
+
z
3
=
3
x
y
z
, when
x
+
y
+
z
=
0
Calculation:
Let x = a – b, y = b – c and z = c – a
Now,
⇒ x + y + z = a – b + b – c + c – a
⇒ x + y + z = 0
⇒
x
3
+
y
3
+
z
3
=
3
x
y
z
⇒
(
a
−
b
)
3
+
(
b
−
c
)
3
+
(
c
−
a
)
3
3
(
a
−
b
)
(
b
−
c
)
(
c
−
a
)
=
3
(
a
−
b
)
(
b
−
c
)
(
c
−
a
)
3
(
a
−
b
)
(
b
−
c
)
(
c
−
a
)
=
1
∴ The value of the
(
a
−
b
)
3
+
(
b
−
c
)
3
+
(
c
−
a
)
3
3
(
a
−
b
)
(
b
−
c
)
(
c
−
a
)
is 1.
© examsnet.com
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