Question

if x=2+ root3 then x+1/x​

Answer 1

Answer:

Step-by-step explanation:

$x = 2 + \sqrt3$

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

$(2 + \sqrt3) + \frac{1}{(2 + \sqrt3)}$

$Take$  $L.C.M$

$\frac{(2 + \sqrt3)^2 + 1}{2 + \sqrt3}$

$\frac{4 + 3 + 4\sqrt3 + 1}{2 + \sqrt 3}$

$\frac{8 + 4\sqrt3}{2 + \sqrt3}$   ----------> this can be answer but, if we can further solve by rationalisation also we will get another answer

Rationalisation

$\frac{8 + 4\sqrt3}{2 + \sqrt3}$ × $\frac{2 - \sqrt3}{2 - \sqrt3}$

$\frac{(8 + 4\sqrt3)(2 - \sqrt3)}{(2 + \sqrt3)(2 - \sqrt3)}$

$\frac{16 - 8\sqrt3 + 8\sqrt3 - 4*3}{(4-3)}$

$4$     -----------------> this is the answer most probably may be given in you book

Hope this helps You

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Answer 2

Answer:

than answer is 4

Step-by-step explanation:

1/x=1/(2+√3)*(2-√3)/(2-√3)

[(a-b) a+b) =(a^2-b^2)]

1/x=(2-√3)

now,

x+1/x=(2+√3)+(2-√3)

x+1/x=2+2+√3-√3

x+1/x=4