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Byju's Answer
Standard VII
Mathematics
Expression Formation
If x-1x2=25...
Question
If
(
x
−
1
x
)
2
=
25
, find the value of
x
2
−
1
x
2
.
Open in App
Solution
We can see that
x
−
1
x
=
5
Also,
(
x
−
1
x
)
2
+
4
=
29
⇒
(
x
+
1
x
)
2
=
29
⇒
x
+
1
x
=
√
29
Now,
x
2
−
1
x
2
=
(
x
−
1
x
)
(
x
+
1
x
)
=
5
√
29
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