Question

x^2+1/x^2 if x=2+root3

Answer 1

Step-by-step explanation:

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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

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Answer 2

Answer:

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

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