If x=5+2root6, find x^2+1/x^2.
Answers
Answered by
0
Answer:
98
Step-by-step explanation:
We know, x
2
+
x
2
1
=(x−
x
1
)
2
+2
Given, x=5−2
6
.
Then,
x
1
=
5−2
6
1
=
(5−2
6
)(5+2
6
)
5+2
6
=
5
2
−(2
6
)
2
5+2
6
=
25−24
5+2
6
=
1
5+2
6
=5+2
6
.
Then, x
2
+
x
1
=(5−2
6
−(5+2
6
))
2
+2
∴(−4
6
)
2
+2=96+2=98.
Therefore, the required value is 98.
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