Question

if a= 2+ root 3 , find the value of a +1/ a​

Answer 1

Answer:

Step-by-step explanation:

Gn: a= 2+root3

To find: a+1/a

2+root3+1/2+root3

(After taking L.C.M)

(2+root3)^2+1/2+root3

=> 4+3+1+4root3/2+root3

=> 8+4root3/2+root3

By rationalising the denominator,

=> 8+4root3(2-root3)/2+root3(2-root3)

=> 16+8root3-8root3-12/4-3

=> 4...........

Answer 2

Step-by-step explanation:

a = 2 + √3

find a + 1 /a

then 1/a = 1 / 2+√3

on rationalising the denominator

( 1/2+√3 ) × 2 -√3/2 -√3

= 2 - √3 ÷ ( 2 )² - (√3)²

= 2 -√3 ÷ 4 - 3

= 2 - √3 / 1

= 2 - √3

now a + 1/a = (2 + √3 ) + ( 2 - √3)

= 2 + √3 +2 -√3

= 4