Question

If a = 7-4√3 Find :- (a) 5/a (b) x-1/x​

Answer 1

Answer:

Step-by-step explanation:

x = 7 + 4√3

To find :

√x + 1 / √x

Solution :

x = 7 + 4√3

⇒ x = 4 + 3 + 4√3

⇒ x = 2² + √3² + 2 × 2 × √3

⇒ x = ( 2 + √3)²

⇒ √x = 2 + √3

Now,

1 / √x = 1 / 2 + √3 × 2 - √3 / 2 - √3

⇒ 1 / √x = 2 - √3 / 2² - √3²

⇒ 1 / √x = 2 - √3 / 4 - 3

⇒ 1 / √x = 2 - √3

Again,

√x + 1 / √x = 2 + √3 + 2 - √3

⇒ √x + 1 / √x = 2 + 2

⇒ √x + 1 / √x = 4

Hence,

√x + 1 / √x = 4

√

Answer 2

Answer:

35+20√3

Step-by-step explanation:

a=7-4√3 (Given)

(a) 5/a

= 5/7-4√3

we want to rationalise this

so..

5/7-4√3 *7+4√3 /7+4√3

=35+20√3/49-48

=35+20√3/1

=35+20√3