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KVPY SA Exam 2011 Question Paper
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© examsnet.com
Question : 3
Total: 80
If
x
+
1
x
=
a
,
x
2
+
1
x
3
=
b
, then
x
3
+
1
x
2
is
a
3
+
a
2
−
3
a
−
2
−
b
a
3
−
a
2
−
3
a
+
4
−
b
a
3
−
a
2
+
3
a
−
6
−
b
a
3
+
a
2
+
3
a
−
16
−
b
Validate
Solution:
x
+
1
x
=
a
and
x
2
+
1
x
3
=
b
(
x
+
1
x
)
2
=
a
2
⇒
x
2
+
1
x
2
+
2
=
a
2
....(1)
and
(
x
+
1
x
)
3
=
a
3
⇒
x
3
+
1
x
3
+
3
x
.
1
x
(
x
+
1
x
)
=
a
3
.
.
.
(
2
)
adding (1) & (2)
(
x
2
+
1
x
3
)
+
(
x
3
+
1
x
2
)
+
2
+
3
(
x
+
1
x
)
=
a
2
+
a
3
b
+
(
x
3
+
1
x
2
)
+
2
+
3
a
=
a
2
+
a
3
∴
x
3
+
1
x
2
=
a
3
+
a
2
−
3
a
−
2
−
b
© examsnet.com
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