Here are the solutions for the visible questions from the image.

Question 21

Given:
$x + \frac{1}{x} = 7$
To find:
$x^2 - \frac{1}{x^2}$

Solution:

1. Square both sides of $x + \frac{1}{x} = 7$:
   $\left( x + \frac{1}{x} \right)^2 = 7^2$
   Expand the square:
   $x^2 + 2 + \frac{1}{x^2} = 49$
2. Subtract $2$ from both sides:
   $x^2 + \frac{1}{x^2} = 49 - 2 = 47$

Thus, the value of $x^2 - \frac{1}{x^2}$ is:
$x^2 - \frac{1}{x^2} = \left( x^2 + \frac{1}{x^2} \right) - 2 \cdot \frac{1}{x^2}$

The correct answer is $47$