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If x + 1/x = 2, then what is value of x - 1/x ?
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- 0
- 1
- 2
- -2
Correct Option: A
Given that, x + 1/x = 2 ...................(i)
On squaring both sides, we get
(x + 1/x)2 = 4
⇒ x2 + 1/x2 + 2 = 4
⇒ x2 + 1/x2 = 2 ..................................(ii)
Now, we have
(x - 1/x)2 = (x2 + 1/x2) - 2x X 1/x
now put the value of x2 + 1/x2
(x - 1/x)2 = 2 - 2 = 0 [from Eq. (ii)]
∴ x - 1/x = 0
