If x^2-1/x^2=38 than what will be x-1/x.

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Solution

Let x - 1/x = z
Then:
z² = (x - 1/x)² = x² - 2 + 1/x²
z² + 2 = x² + 1/x²

Since we are told:
x² + 1/x² = 38
z² + 2 = 38
z² = 36
z = ±6
x - 1/x = ±6

So there are two possible values for x-1/x : 6 and -6

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