Question

 If x = ( 2+ √3 ) , find the value of ( x^2 + 1/x² )²
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Answer 1

Answer:

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Step-by-step explanation:

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Given :

x = 2 + √3

To find :

x² + 1 / x²

Solution ;

x = 2 + √3

⇒ 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

Now,

x + 1 / x = 2 + √3 + 2 - √3

⇒ x + 1 / x = 2 + 2

⇒ x + 1 / x = 4

And, on squaring both sides.

( x + 1 / x ) ² = (4)²

⇒ x² + 1 / x² + 2 = 16

⇒ x² + 1 / x² = 16 - 2

⇒ x² + 1 / x² = 14.

Hence,

x² + 1 / x² = 14.

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