Question

if X=3+√5 , find the value of X+1/x​

Answer 1

Answer:

Step-by-step explanation:

x=3+√5

$\frac{1}{x} = \frac{1}{3+\sqrt{5} }$

$\frac{1}{3+\sqrt{5} } = (\frac{1}{3+\sqrt{5}} )( \frac{3-\sqrt{5} }{3-\sqrt{5} })$

$= \frac{3-\sqrt{5} }{3^{2} - \sqrt{5} ^{2} }$  [(a+b)(a-b)=$a^{2}-b^{2}$]

$= \frac{3-\sqrt{5} }{3^{2} - \sqrt{5} ^{2} } = \frac{3-\sqrt{5} }{4 }$

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

$(3+\sqrt{5} )+ \frac{3-\sqrt{5} }{4} \\= \frac{12+4\sqrt{5}+3-\sqrt{5} }{4} \\= \frac{15+3\sqrt{5} }{4}$