Question

If x^2+1/x =31/3
Find x-1/x

Answer 1

see above attachment for your required answer

Answer 2

Answer: 25$\sqrt{3}$/3

Step-by-step explanation:

by (a - b)^2 = a^2 + b^2 - 2*a*b

comparing with x^2 + 1 / x^2

=> (x - 1/x)^2 = x^2 + 1/x^2 -2*x* 1/x

=> (x - 1/x)^2 = 31/3 - 2 [since x^2 + 1/x^2 = 31/3 (given)]

=>  (x - 1/x)^2 = 31/3 - 6/3

=>  (x - 1/x)^2 = 25/3

=>  x - 1/x = 25/$\sqrt{3}$

now making denominator rational by rationalisation

= 25/$\sqrt{3}$ * $\sqrt{3}$/$\sqrt{3}$

= 25$\sqrt{3}$/3

hope this helps you