Question

if x=7+4√3 then find the value of √x+1/√x

Answer 1

I hope you will be able to understand

Answer 2

Hey mate !

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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

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Thanks for the question!

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