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SSC CGL Tier 2 Exam 25 Oct 2015 Paper 1
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© examsnet.com
Question : 2
Total: 100
Let
x
=
√
13
+
√
11
√
13
−
√
11
and
y
=
1
x
then the value of
3
x
2
−
5
x
y
+
3
y
2
is
1717
1177
1771
1171
Validate
Solution:
(1)
x
=
√
13
+
√
11
√
13
−
√
11
On rationalising the denominator
=
√
13
+
√
11
√
13
−
√
11
×
√
13
+
√
11
√
13
+
√
11
=
(
√
13
+
√
11
)
2
(
√
13
)
2
−
(
√
11
)
2
=
13
+
11
+
2
143
13
−
11
=
24
+
2
√
143
2
=
12
+
√
143
∴
y
=
1
x
=
1
12
+
√
143
=
1
12
+
√
143
×
12
−
√
143
12
−
√
143
=
12
−
√
143
144
−
143
=
12
−
√
143
∴
x
−
y
=
12
+
√
143
−
12
+
√
143
=
2
√
143
and
x
y
=
(
12
+
√
143
)
(
12
−
√
143
)
=
144
−
143
=
1
∴
3
x
2
−
5
x
y
+
3
y
2
=
3
x
2
−
6
x
y
+
3
y
2
+
x
y
=
3
(
x
−
y
)
2
+
x
y
=
3
(
2
√
143
)
2
+
1
=
3
×
4
×
143
+
1
=
1716
+
1
=
1717
© examsnet.com
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