Question

hii


if x = 2 + √3


find x² + 1/x² and x³ + 1/x³


plzz, it is branliest question...

Answer 1

Hi there !

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Given :

x = 2 + √3

To Find :

(i) x² + 1 / x²

(ii) x³ + 1 / x³

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x = 2 + √3

1 / x = 1 / 2 + √3

1 / x = 1 / 2 + √3 × 2 - √3 / 2 - √3

1 / x = 2 - √3 / (2)² - (√3)²

1 / x = 2 - √3 / 4 - 3

1 / x = 2 - √3

Now,

x + 1 / x = 2 + √3 + 2 - √3

x + 1 / x = 2 + 2

x + 1 / x = 4  

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Question I :

x + 1/x = 4

On squaring both sides ..

( x + 1/x )² = (4)²

x² + 1 / x² + 2 = 16

x² + 1 / x² = 16 - 2

x² + 1 / x² = 14  [Ans]

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Question II :

x + 1 / x = 4

On cubing both sides ..

( x + 1/x )³ = (4)³

x³ + 1/x³ + 3 ( x + 1/x) = 64

x³ + 1/x³ + 3 (4) = 64

x³ + 1/x³ + 12  = 64

x³ + 1/x³ = 64 - 12

x³ + 1/x³ = 52  [Ans]

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Thanks for the question !

Answer 2

Heya!!

If x = 2 + √3

=) 1/x = 1/(2+√3) * (2-√3)/2-√3

= 2-√3 / (2^2 - √3^2)

= 2-√3

Since x^2 + 1/x^2

= (x + 1/x)^2 - 2*x*1/x

= (x +1/x)^2 - 2

= (2 + √3 + 2 - √3) ^2 - 2

= 4^2 - 2

= 16-2

= 14

2) x^3 + 1/x^3

= (2 + √3) ^3 + (2-√3)^2

= 8 + 3√3 + 12√3 + 18 + 8 - 3√3 - 12√3 + 18

= 52

Hope it helps uh!!