Question

If x=7+4√3, find the value of √x+1/√x

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Answer 1

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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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