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KVPY SA Exam 2013 Question Paper
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© examsnet.com
Question : 5
Total: 80
Let x,y,z be non-zero real numbers such that
x
y
+
y
z
+
z
x
=
7
and
y
x
+
z
y
+
x
z
=
9
then
x
3
y
3
+
y
3
z
3
+
z
3
x
3
−
3
is equal to
152
153
154
155
Validate
Solution:
a
3
+
b
3
+
c
3
−
3
a
b
c
=
[
a
+
b
+
c
]
[
(
a
+
b
+
c
)
2
−
3
(
a
b
+
b
c
+
c
a
)
]
=
[
7
]
[
(
7
)
2
−
3
(
9
)
]
=
7
(
49
−
27
)
=
7
×
22
=
154
© examsnet.com
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