Question

if x²+1/x²=66 find the value of x-1/x

Answer 1

Solution:-

given:-

x²+1/x²=66


${x}^{2} + \frac{1}{ {x}^{2} } = {(x - \frac{1}{x}) }^{2} + 2 \\ {(x - \frac{1}{x}) }^{2} = 66 - 2 \\ (x - \frac{1}{x} ) = \sqrt{64} \\ (x + \frac{1}{x} ) = 8$

Answer 2

Answer:

Value of x - 1/x is 8

Step-by-step explanation:

Given,

x² + 1/ x² = 66

Apply (a - b)² = a² + b² - 2 a b

Here a = x

and b = 1/x

(x - 1/x)² = x² + 1/x² - 2

= 66 - 2

(x - 1/x)² = 64

x - 1/x = √ 64

= 8

Value of x - 1/x is 8