Question

If x² + 1/x²= 66, find the value of x - 1/x

Answer 1

Answer:

Please see the attachment

Answer 2

Given :  x² + 1/x² = 66

We know that, (x - 1/x)² = x² + (1/x)² - 2 × x × 1/x  

[By using identity , (a - b)²  = a² + b² - 2ab]

(x - 1/x)² = x² + (1/x)² - 2  

(x - 1/x)² =66 - 2

(x - 1/x)² = 64

(x - 1/x) = ±√64

[Taking square root on both sides]

x - 1/x = ±8

Hence the value of x - 1/x is ±8.  

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