Question

If X square + 1 by x square is equal to 27 find X + 1 by x and x minus one by X

Answer 1

Answer:

$x {}^{2} + \frac{1}{x {}^{2} } = 27 \\ = > (x + \frac{1}{x} ) {}^{2} = x {}^{2} + \frac{1}{x {}^{2} } + 2 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \: 27 + 2 = 29 \\ so \: \: \: (x + \frac{1}{x} ) = \sqrt{29} \\ \\ now \: \: (x - \frac{1}{x} ) {}^{2} = x {}^{2} + \frac{1}{x {}^{2} } - 2 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 27 - 2 = 25 \\ hence \: \: (x - \frac{1}{x} ) = \sqrt{25} = 5$