Question

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Answer 1

Heya Dear,

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Q . If x = 2 - √3 , find ( x + 1/x )³.

Given,

  x = 2 - √3

∴ 1/x = 1/( 2 - √3 )

By multiplying the denominator and numerator of R.H.S by ( 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 )³

= ( 2 - √3 + 2 + √3 )³

= ( 4 )³ 

= 64.

The required answer is 64.


Hope it helps !

By : Vaibhav

Answer 2

$Given: x = 2 - \sqrt{3}$

$= \ \textgreater \ \frac{1}{x} = \frac{1}{2 - \sqrt{3} } * \frac{2 + \sqrt{3} }{2 + \sqrt{3} }$

$= \ \textgreater \ \frac{2 + \sqrt{3} }{2^2 - ( \sqrt{3})^2 }$

$= \ \textgreater \ \frac{2 + \sqrt{3} }{4 - 3}$

$= \ \textgreater \ 2 + \sqrt{3}$


Now,

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

                             = 4.


Then,

$(x + \frac{1}{x} )^3 = (4)^3$

                                   = 64.


Hope this helps!