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Standard XII
Mathematics
Question
x
=
√
5
−
2
√
5
+
2
and
y
=
√
5
+
2
√
5
−
2
.
If
x
2
is
161
−
72
√
m
, then value of
m
is ?
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Solution
Verified by Toppr
Given,
x
2
is
161
−
72
√
m
.............(1)
Rationalize the denominator,
x
=
√
5
−
2
√
5
+
2
×
√
5
−
2
√
5
−
2
x
=
5
+
4
−
4
√
5
5
−
4
x
=
9
−
4
√
5
1
.
x
2
=
(
9
−
4
√
5
)
(
9
−
4
√
5
)
=
81
+
16
×
5
−
72
√
5
=
161
−
72
√
5
....................(2)
Comparing equations (1) and (2), we get,
m
=
5
.
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Q1
x
=
√
5
−
2
√
5
+
2
and
y
=
√
5
+
2
√
5
−
2
.
If
x
2
is
161
−
72
√
m
, then value of
m
is ?
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, then the value of
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