Question

please solve this.
Chapter- Expansions​

Answer 1

Answer:

$lets \: \: first \: \: find \: \: the \: \: value \: \: of \: x \\ x - \frac{1}{x} = \sqrt{5} \\ squaring \: \: both \: \: sides \\ (x - \frac{1}{x} {)}^{2} = ( \sqrt{5} {)}^{2} \\ \\ we \: \: will \: \: use \: \: this \: \: identity \: \: now \\ (x - y {)}^{2} = {x}^{2} + {y}^{2} - 2xy \\ \\ (x {)}^{2} + ( \frac{1}{x} {)}^{2} - 2 \times x \times \frac{1}{x} = 5 \\ {x}^{2} + \frac{1}{ {x}^{2} } - 2 = 5 \\ {x}^{2} + \frac{1}{{x}^{2} } = 5 + 2\\ {x}^{2} + \frac{1}{ {x}^{2} } = 7 \: \: \: \\ this \: \: is \: \: the \: \: answer \: \: of \: \: first \: \\ part \\ {x}^{2} + \frac{1}{ {x}^{2} } = 7 \\ (x + \frac{1}{x} {)}^{2} = 7 \\ x + \frac{1}{x} = \sqrt{7}$

I hope it will help you

Answer 2

Answer:

Answer :-

(i) $x^2 + \frac{1}{x^2} = 7$

(ii) $x + \frac{1}{x} = \sqrt{7}$