Question

If x=2 + √3,then find the value of x² + 1/x².
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Answer 1

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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,

x² = (2+√3)

(2)² + (√3)² + 2×2× √3 =

= 4 + 3 + 4√3

= 7+ 4√3

1/x²=(2-√3)²

= (2)² + (√3)² - 2×2× √3

= 4 + 3 - 4√3

= 7 - 4√3

x²+1/x²

= (7 + 4√3) + (7 - 4√3)

= 7+ 4√3+7-4√3

= 7 + 7 + 4√3 - 4√3

= 14

• I Hope it's Helpful My Friend.

Answer 2

Step-by-step explanation:

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,

x² = (2+√3)

(2)² + (√3)² + 2×2× √3 =

= 4 + 3 + 4√3

= 7+ 4√3

ANSWER