Question

If x square + 1/x square = 47, then find x + 1/x and x - 1/x

Answer 1

${x}^{2} + \frac{1}{ {x}^{2} } = 47$

Now, adding 2 in first equation, we get

${x}^{2} + \frac{1}{ {x}^{2} } + 2 = 47 + 2$

$({x + \frac{1}{x} })^{2} = 49$

$x + \frac{1}{x} = \sqrt{49}$

$x + \frac{1}{x} = 7$

That's the first answer

Then,
Subtracting 2 in the first equation, we get

${x}^{2} + {1/x}^{2} - 2 = 47 - 2$

$({x - 1/x})^{2} = 45$

$x - 1/x = \sqrt{45}$

That makes up the second answer.
Hope these help to you.