If x = 4-√15,then the value of (x+1/x) is
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Answer:
x+1/x=8.
Step-by-step explanation:
We are given that x=4+
15
, so we first find
x
1
as shown below:
x
1
=
4+
15
1
=
4+
15
1
×
4−
15
4−
15
(Rationalising)
=
(4+
15
)(4−
15
)
4−
15
=
4
2
−(
15
)
2
4−
15
(∵(a+b)(a−b)=a
2
−b
2
)
=
16−15
4−
15
=
1
4−
15
=4−
15
Therefore,
x
1
=4−
15
Now, let us find x+
x
1
as follows:
x+
x
1
=4+
15
+4−
15
=8
Hence, x+
x
1
=8.
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