Question

If X = 2 + √5 Find the value of x^2 - 1/x^2

Answer 1

Step-by-step explanation:

$= {x}^{2} - \frac{1}{ {x}^{2} } \\ = {(2 + \sqrt{5} )}^{2} - \frac{1}{(2 + \sqrt{5})^{2}} \\ = 4 + 4 \sqrt{5} + 5 - \frac{1}{4 + 4 \sqrt{5} + 5} \\ = 4 \sqrt{5} + 9 - \frac{1}{4 \sqrt{5} + 9 } \\ = \frac{( {4 \sqrt{5} + 9})^{2} - 1}{4 \sqrt{5} + 9 } \\ = \frac{80 + 72 \sqrt{5 }+81 - 1}{4 \sqrt{5} + 9} \\ = \frac{160 - 72 \sqrt{5} }{4 \sqrt{5} + 9 }$