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Byju's Answer
Standard X
Mathematics
Rational Numbers
If x=3+22, ch...
Question
If
x
=
3
+
2
2
, check whether
x
+
1
x
is rational or irrational.
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Solution
x
=
3
+
2
2
.
.
.
.
.
1
⇒
1
x
=
1
3
+
2
2
⇒
1
x
=
1
3
+
2
2
×
3
-
2
2
3
-
2
2
⇒
1
x
=
3
-
2
2
3
2
-
2
2
2
⇒
1
x
=
3
-
2
2
9
-
8
⇒
1
x
=
3
-
2
2
.
.
.
.
.
2
Adding (1) and (2), we get
x
+
1
x
=
3
+
2
2
+
3
-
2
2
=
6
, which is a rational number
Thus,
x
+
1
x
is rational.
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