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Question

If x2+1x2=27, find x-1x.


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Solution

Compute the required value.

As we know that, a-b2=a2+b2-2ab.

x-1x2=x2+1x2-2x×1xx-1x2=27-2x-1x2=25

Take square root on both sides.

x-1x=±25

Hence, the value of x-1x is ±5.


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