If x=√2+1, find the value of x^3+1/x^3?
Answers
Answered by
1
Answer:
Step-by-step explanation:
140
√
2
.
Explanation:
We are given that,
x
=
3
+
2
√
2
.
∴
1
x
=
1
3
+
2
√
2
=
1
3
+
2
√
2
×
1
,
=
1
3
+
2
√
2
×
3
−
2
√
2
3
−
2
√
2
,
=
3
−
2
√
2
3
2
−
(
2
√
2
)
2
=
3
−
2
√
2
9
−
8
.
⇒
1
x
=
3
−
2
√
2
.
Hence,
x
2
+
1
x
2
=
(
3
+
2
√
2
)
2
+
(
3
−
2
√
2
)
2
,
=
2
{
3
2
+
(
2
√
2
)
2
}
.
⇒
x
2
+
1
x
2
=
34
.
Thus, we have,
x
−
1
x
=
4
√
2
,
and
,
x
2
+
1
x
2
=
34
.
Finally,
x
3
−
1
x
3
=
(
x
−
1
x
)
(
x
2
+
1
+
1
x
2
)
,
=
(
4
√
2
)
(
34
+
1
)
=
140
√
2
.
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