if x2 + 1/x2 = 27, find the values of each of the follwing. x+¹/x x-1/x
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Answer:
x−
x
1
We have,
(x−
x
1
)
2
=x
2
−2×x×
x
1
+
x
2
1
⇒(x−
x
1
)
2
=x
2
−2+
x
2
1
⇒(x−
x
1
)
2
=x
2
+
x
2
1
−2
⇒(x−
x
1
)
2
=27−2[∵x
2
+
x
2
1
=27 given]
⇒(x−
x
1
)
2
=25⇒(x−
x
1
)
2
⇒x−
x
1
=±5
[Taking square root of both sides]
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