Hello,

Here is the solution :-

We are given:

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

Step 1: Use Identity

We use the identity:

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

Substituting the given value:

(x + 1/x) ^ 2 = 14 + 2 = 16

Step 2: Solve for x + 1/x

Taking the square root:

x + 1/x = ±4

Answer:

x + 1/x = ±4

Hope it helps !