Question

If x=2+root 3, find the value of x+1/x

Answer 1

$x = 2 + \sqrt{3} \\ x = 2 + \sqrt{3} \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } \\ x = {2}^{2} - { \sqrt{3} }^{2} \div 2 - \sqrt{3} \\ x = \frac{1}{2 - \sqrt{3} } \\ \frac{1}{x} = 2 - \sqrt{3} \\ \\ x + \frac{1}{x} = 2 + \sqrt{3} + 2 - \sqrt{3} = 4$

Answer 2

HEYA ❤️

x=2+√3

1/x = 1/2+√3

by rationalizing the denominator,

1/x= 2-√3

HENCE,

(x+1/x)= 2+√3+2-√3

(√3 and -√3 are cancelled out )

THEREFORE,

x+1/x= 2+2 = 4 (REQUIRED ANSWER)

HOPE IT HELPS ❤️