If x2 + 1/x^2 = 27 find the values of each of the following: (i) x + 1/x (ii) x - 1/x
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Answer:
If x
2
+
x
2
1
=27, find the value of x−
x
1
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
Step-by-step explanation:
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