Question

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

Answer 1

Answer:

x = 2+ √3

$\frac{1}{x} = \frac{2 - \sqrt{3} }{4 - 3} = 2 - \sqrt{3}$

${x}^{2} + \frac{1}{ {x}^{2} } \\ \\ = 2 + \sqrt{3 } + 2 - \sqrt{3} \\ = 4$

Answer 2

Answer:

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

Step-by-step explanation:

hope it's helps you