Question

if x2 +1/x2 = 14 then x2-1/x2 = ?

Answer 1

$\underline\bold{\huge{ANSWER \: :}}$

GIVEN, x² + 1/x² = 14.
______________________________

We know, a²+b² = (a+b)² - 2 ab

So, (x+1/x) ² - 2 = 14

=> (x+1/x) = √16 = 4

______________________________

We also know, a²+b² = (a-b)² + 2 ab

So, (x-1/x)² + 2 = 14

=> (x - 1/x) = √12

______________________________

Ultimately, x² - 1/x²

= (x + 1/x) (x - 1/x)

= 4√12 [ANSWER]

Answer 2

Answer:

+/-8root3

Step-by-step explanation:

X^2 + 1/X^2 = 14

We need to find out

X^2 - 1/X^2

(X+1/X)^2 = X^2 + 1/ X^2 + 2X/X

(X+1/X^2) = 14 + 2

(X + 1/X)^2 = 16

(X +1/X) = +/- 4

(X -1/X)^2 = X^2 + 1/X^2 - 2X/X

(X-1/X)^2 = 14 -2

(X-1/X)^2 = 12

(X-1X) = +/- 2root3

X^2 - 1/X^2 = (X+1/X)(X-1/X)

X^2 - 1/X^2 = (+/-4)(+/-2root3)

= +/- 8root3