Question

hello

x = 7 + 4√3

find ..

√x + 1/√x

thanku

Answer 1

Hi there !

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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 = (2)² + (√3)² + 2 × 2 × √3

Using Identity :

a² + b² + 2ab = (a + b)²

⇒( 2 + √3 )²

Now,

√x = √ (2 + √3)²

√x = 2 + √3

And,

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

Ciao user!!


$<b> x = 7 + 4 √3</b>$

$<b>=> x = 4 + 3 + 4√3 </b>$

$<b> => x = (2)^2 + (√3)^2 + 2.2.√3 </b>$

$<b> Using formula, a^2 + b^2 + 2ab </b>$

$<b> (2+√3)^2 </b>$

$<b> Now,</b>$


$<b> √x = √(2+√3)^2 </b>$


$<b> √x = (2+√3)</b>$

Also,


$<b> 1/√x = 1/2 + √3×2 - √3/2 -√3 </b>$

$<b> 1/√x = 2 - √3/2 ^2 - √3^2</b>$

$<b> 1/√x = 2 - √3/4 - 3</b>$

$<b> 1/√x = 2-√3 </b>$

$<b> Again , </b>$

$<b> √x+1/√x = 2+√3 + 2-√3 </b>$

$<b> √x+1/√x = 2+2</b>$

$<b> √x+1/√x = 4</b>$


$<b> Hence, √x+1/√x = 4</b>$

Hope this help!!!!