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Manipal Entrance Test 2015 Math Paper
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© examsnet.com
Question : 70
Total: 70
The number of positive integral solutions of
x
2
+
9
<
(
x
+
3
)
2
<
8
x
+
25
,
is
2
3
4
5
Validate
Solution:
We have,
x
2
+
9
<
(
x
+
3
)
2
<
8
x
+
25
⇒
x
2
+
9
<
x
2
+
6
x
+
9
<
8
x
+
25
⇒
x
2
+
9
<
x
2
+
6
x
+
9
and
x
2
+
6
x
+
9
<
8
x
+
25
⇒
6
x
>
0
and
x
2
−
2
x
−
16
<
0
⇒
x
>
0
and
1
−
√
17
<
x
<
1
+
√
17
⇒
0
<
x
<
1
+
√
17
∴
x
=
1
,
2
,
3
,
4
,
5
© examsnet.com
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