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Standard IX
Mathematics
Algebraic Identities
Question
If
x
2
+
1
x
2
=
51
, find the value of
x
3
−
1
x
3
Open in App
Solution
Verified by Toppr
a
3
−
b
3
=
(
a
−
b
)
(
a
2
+
b
2
+
a
b
)
So,
x
3
−
1
x
3
=
(
x
−
1
x
)
(
x
2
+
1
x
2
+
x
×
1
x
)
=
(
x
−
1
x
)
(
x
2
+
1
x
2
+
1
)
=
(
x
−
1
x
)
(
51
+
1
)
=
52
(
x
−
1
x
)
Now,
(
x
−
1
x
)
2
=
x
2
+
1
x
2
−
2
x
×
1
x
(
x
−
1
x
)
2
=
51
−
2
=
49
x
−
1
x
=
√
49
=
7
Therefore,
x
3
−
1
x
3
=
52
(
x
−
1
x
)
=
52
×
7
=
364
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