x²+1/x² = 7 হলে, x³+1/x³=?
Answers
Answered by
0
Given:
x
2
+
1
x
2
=
7
Adding
2
on both the sides, we get,
⇒
x
2
+
1
x
2
+
2
=
7
+
2
⇒
x
2
+
1
x
2
+
2
×
x
×
1
x
=
9
⇒
(
x
+
1
x
)
2
=
3
2
⇒
x
+
1
x
=
±
3
∴
x
+
1
x
=
3
Cubing both the sides, we get,
⇒
(
x
+
1
x
)
3
=
3
3
⇒
x
3
+
1
x
3
+
3
(
x
)
(
1
x
)
(
x
+
1
x
)
=
27
⇒
x
3
+
1
x
3
+
3
(
3
)
=
27
⇒
x
3
+
1
x
3
=
27
−
9
∴
x
3
+
1
x
3
=
18
Similar questions