Question

I want the answer of part i .with full solution. best answer that i can understand can b marked as brainliest .

Answer 1

a =3+√8
a^2=(3)^2+(√8)^2+6√8
      =9+8+6√8
       =17+6√8
1/a^2=17-6√8
a^2+1/a^2=17+17=34

Answer 2

$Given : a = 3 + \sqrt{8}$

$= \ \textgreater \ a^2 = (3 + \sqrt{8} )^2$

$= \ \textgreater \ 9 + 8 + 12 \sqrt{2}$

$= \ \textgreater \ 17 + 12 \sqrt{2}$

Now,

$= \ \textgreater \ \frac{1}{a^2} = \frac{1}{17 + 12 \sqrt{2} } * \frac{17 - 12 \sqrt{2} }{17 - 12 \sqrt{2} }$

$= \ \textgreater \ \frac{(1)(17 - 12 \sqrt{2}) }{(17)^2 - (12 \sqrt{2} )^2}$

$= \ \textgreater \ \frac{17 - 12 \sqrt{2} }{289 - 288}$

$= \ \textgreater \ 17 - 12 \sqrt{2}$

Therefore:

$= \ \textgreater \ a^2 + \frac{1}{a^2} = 17 + 12 \sqrt{2} + 17 - 12 \sqrt{2}$

= > 17 + 17

= > 34.



Hope this helps!