Question

if x = 7 + 4root3, find rootx + 1 / rootx

Answer 1

Hey mate !

_______________________

Given :

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

_______________________

Thanks for the question!

☺️☺️☺️

Answer 2

Hey mate !

_______________________

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

_______________________

Thanks for the question!

@Aaisha44 ❤️