Question

if x = 3+ root 8, show that
[x square + 1 by x square] = 34

Answer 1

Hi ,

x = 3 + √8 ,

1/x = 1/( 3 + √8 )

= ( 3 - √8 )/[ ( 3 + √8 )( 3 - √8 ) ]

= ( 3 - √8 )/[ ( 3² - ( √8 )²

= ( 3 - √ 8 )/ ( 9 - 8 )

= 3 - √8

x + 1/x = 3 + √8 + 3 - √8 = 6

Now ,

LHS = x² + 1/x² = ( x + 1/x )² - 2

= 6² - 2

= 36 - 2

= 34

= RHS

Hence proved.

I hope this helps you.

: )

Answer 2

Given x = 3 root 8.

Now,

$= \ \textgreater \ \frac{1}{x} = \frac{1}{3 + \sqrt{8} } * \frac{3 - \sqrt{8} }{3 - \sqrt{8} }$


$= \ \textgreater \ \frac{3 - \sqrt{8} }{(3)^2 - ( \sqrt{8} )^2}$

$= \ \textgreater \ \frac{3 - \sqrt{8} }{9-8}$

$= \ \textgreater \ 3 - \sqrt{8}$

Now,

$x + \frac{1}{x} = 3 + \sqrt{8} + 3 - \sqrt{8}$

                             = 6.



Therefore:

$= \ \textgreater \ (x^2 + \frac{1}{x^2} ) = (x + \frac{1}{x})^2 - 2 * x * \frac{1}{x}$

$= \ \textgreater \ 6^2 - 2$

= > 36 - 2

= > 34.


Hope this helps!