Question

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

Answer 1

Heya ☺

Given that

x = 2 + √3

1/x = 1/2 + √3

= 1 × (2 - √3)/(2 + √3) (2 - √3)

= (2 - √3)/(2^2 - √3^2)

= (2 - √3)/4 - 3

= (2 - √3)

Therefore ,

x^2 = (2 + √3)

= (2)^2 + (√3)^2 + 2 × 2 × √3

= 4 + 3 + 4√3

= 7 + 4√3

1/x^2 = (2 - √3)^2

= (2)^2 + (√3)^2 - 2 × 2 × √3

= 4 + 3 - 4√3

= 7 - 4√3

x^2 + 1/x^2

= (7 + 4√3) + (7 - 4√3)

= 7 + 4√3 + 7 - 4√3

= 7 + 7 + 4√3 - 4√3

= 14

Thanks