Question

hi



I have heard many things about this app, so plz help me if you can. if x is equal to 2 plus root 3. find x square plus 1 by x square.


Thanku ...

Answer 1

Hi there !

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Given :

x = 2 + √3

To find :

x² + 1 / x²

Solution :

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

= 2 + 2

= 4

Now,

(x + 1 / x)² = (4)²

=> x² + 1 / x² + 2 = 16

=> x² + 1 / x² = 16 - 2

=> x² + 1 / x² = 14

Hence,

The required answer is

x² + 1 / x² = 14.

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Thanks for the question !

Answer 2

Answer :-

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Given ,

x = 2 + √3

To find ,

• The value of : x² + 1 / x²

Now ,

If ,

x = 2 + √3

Then ,

1 / x = 1 / ( 2 + √3 )

= 1 / ( 2 + √3 ) × ( 2 - √3 ) / ( 2 - √3 )

= ( 2 - √3 ) / { ( 2 )² - ( √3 )² }

= ( 2 - √3 ) / ( 4 - 3 )

= ( 2 - √3 ) / 1

= ( 2 - √3 )

Now ,

( x + 1 / x )

= ( 2 + √3 + 2 - √3 ) [ • Putting the values ]

= 2 + 2

= 4

Therefore ,

x² + 1 / x²

= ( x + 1 / x )² - 2 . x . 1 / x

[ • Using Identity ]

= ( 4 )² - 2 [ • Putting the value ]

= 16 - 2

= 14 [ ★ Required answer ]

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