Question

if x = 3 + √8 find x+1/x²

Answer 1

Since x=3+√8 : -

$\orange{\sf x^{2} +\frac{1}{x^{2}} = x^{2} +\frac{1}{x^{2}} + 2 - 2}$

$\sf = (x + \frac{1}{x} )^{2}  - 2$

$\sf = ( 3 + 2\sqrt{2}  + \frac{1}{3 + 2\sqrt{2} } )^{2}  - 2$

$\sf = ( 3 + 2\sqrt{2}  + \frac{3 - 2\sqrt{2}}{9 - 8} )^{2}  - 2$

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

$\orange{\sf = ( 6 )^{2} - 2 =34}$