Question

if a=7-4√3,find the value of √a+1/√a.

Answer 1

a = 7 - 4root3-----(1)

1/a = 1/(7-4root3)
=(7+4root3)/(7-4root3)(7+4root3)
= (7+4root3)/(49-48)

= 7+4root3-----(2)

(root a + 1/root a)^2 = a+1/a + 2*a*1/a

= 7- 4root 3 +7+4 root3+2[from (1) and (2)]

=14

(root a+1/ root a) = root 14

Answer 2

Answer :

4

Step-by-step explanation :

Find the value of √a :

a = 7 - 4√3

a = 4 + 3 - 4√3

a = (2)² + (√3)² - 2 * 2 * √3

a = ( 2 - √3 )²

By rooting both the sides

√a = √(2 - √3)²

√a = 2 - √3

Find the value of 1 / √a :

√a = 2 - √3

1 / √a = 1 / 2 - √3

1 / √a = 1 / 2 - √3 * 2 + √3 / 2 + √3

1 / √a = 2 + √3 / 2² - √3²

1 / √a = 2 + √3 / 4 - 3

1 / √a = 2 + √3

Find √a + 1 / √a :

√a + 1 / √a = 2 - √3 + 2 + √3

√a + 1 / √a = 2 + 2

√a + 1 / √a = 4

Hence, the answer is 4.