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If x + 1x = 7 , find x^3 + 1x^3 .
Question
If
x
+
x
1
=
7
, find
x
3
+
x
3
1
.
Hard
Open in App
Updated on : 2022-09-05
Solution
Verified by Toppr
It is given that
x
+
x
1
=
7
, by taking cubes on both sides we get:
(
x
+
x
1
)
3
=
7
3
⇒
(
x
)
3
+
(
x
1
)
3
+
(
3
×
x
×
x
1
)
(
x
+
x
1
)
=
3
4
3
(
∵
(
a
+
b
)
3
=
a
3
+
b
3
+
3
a
b
(
a
+
b
)
)
⇒
x
3
+
x
3
1
+
3
(
7
)
=
3
4
3
(
G
i
v
e
n
x
+
x
1
=
7
)
⇒
x
3
+
x
3
1
+
(
3
×
7
)
=
3
4
3
⇒
x
3
+
x
3
1
+
2
1
=
3
4
3
⇒
x
3
+
x
3
1
=
3
4
3
−
2
1
⇒
x
3
+
x
3
1
=
3
2
2
Hence,
x
3
+
x
3
1
=
3
2
2
.
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