Question

If x = 7+3V5 then find 1/x

Answer 1

Step-by-step explanation:

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!

Answer 2

Answer:

$x = 7 + 3 \sqrt{5} \\ 1 \div x = 1 \div (7 + 3 \sqrt{5)} \\ 1 \div x = 7 - 3 \sqrt{5 } \div (7 + 3 \sqrt{5)} (7 - 3 \sqrt{5)} \\ 1 \div x = 7 - 3 \sqrt{5 } \div( 49 - 45) \\ 1 \div x = 7 - 3 \sqrt{5 } \div 4$