Question

Hi !

Answer please

if x = 2 + √3 , find x² + 1/x².

Answer 1

this is the answer of your question

Answer 2

Hey there !

______________________

Given :

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

Squaring both sides ;

( x + 1/x)² = (4)²

=> x² + 1/x² + 2 = 16

=> x² + 1/x² = 16 - 2

=> x² + 1/x² = 14

Thanks for the question!