Find The Value Of x²+1/x²

1.	Find The Value Of x²+1/x²
Answer» Answer: 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 THANKS

Answer»

Answer:

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

THANKS

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