if x = (2+root3) , find the value of x2 +1by x2 Simplify: (root5 - - Maths - Number Systems

Question

if x = (2+root3) , find the value of x2 +1by
x2 Simplify: (root5 - 1 by root5+1 + root5 + 1 by root5
- 1)

Gursheen kaur. · Accepted Answer

$G i v e n : x = 2 + \sqrt{3} n o w, \frac{x^{2} + 1}{x^{2}} = \frac{x^{2}}{x^{2}} + \frac{1}{x^{2}} = 1 + \frac{1}{{(2 + \sqrt{3})}^{2}} = 1 + \frac{1}{4 + 3 + 2 \sqrt{3}} = 1 + \frac{1}{7 + 2 \sqrt{3}} = \frac{7 + 2 \sqrt{3} + 1}{7 + 2 \sqrt{3}} = \frac{8 + 2 \sqrt{3}}{7 - 2 \sqrt{3}}$

$\frac{\sqrt{5} - 1}{\sqrt{5} + 1} + \frac{\sqrt{5} + 1}{\sqrt{5} - 1} = \frac{{(\sqrt{5} - 1)}^{2} + {(\sqrt{5} + 1)}^{2}}{(\sqrt{5} + 1) (\sqrt{5} - 1)} = \frac{5 + 1 - 2 \sqrt{5} + 5 + 1 + 2 \sqrt{5}}{5 - 1} = \frac{12}{4} = 3$

if x = (2+root3) , find the value of x2 +1by x2. Simplify: (root5 - 1 by root5+1 + root5 + 1 by root5 - 1)

if x = (2+root3) , find the value of x²+1by x². Simplify: (root5 - 1 by root5+1 + root5 + 1 by root5 - 1)