Question

Factorise the following:

`x^2 + 1/x^2 - 14`

Answer 1

Given expression: `x^2 + 1/x^2 - 14`

Step-wise calculation:

1. Recognize that `x^2 + 1/x^2 = (x + 1/x)^2 - 2`.

2. Let `y = x + 1/x`.

3. Then, `x^2 + 1/x^2 = y^2 - 2`

4. Substituting back:

`x^2 + 1/x^2 - 14 = (y^2 - 2) - 14`

`x^2 + 1/x^2 - 14 = y^2 - 16`

5. This is a difference of squares:

y² – 16 = (y – 4)(y + 4)

6. Substitute back `y = x + 1/x`: 

`(x + 1/x - 4)(x + 1/x + 4)`