Question

If x=3root6 then find x^2+1/x^2

Answer 1

x = 3√6

x²+1/x²

= (3√6)² + 1/(3√6)²

= (3√6)² = (3√6)*(3√6) = 3*3*6 = 54

so, 54 +1/54

=(2916+1)/54

= 2917/54

Answer 2

Answer:

$\boxed{54\frac{1}{54}}$

Step-by-step explanation:

x = 3√6

1/x = 1/3√6

⇒ 1/x = 1/3√6 × 3√6/3√6

⇒ 1/x = 3√6/54

⇒ 1/x = √6/18

⇒ x² + 1/x² = ( 3√6 )² + ( √6/18 )²

⇒ x² + 1/x² = 9 × 6 + 6/324

⇒ x² + 1/x² = 54 + 1/54

⇒ x² + 1/x² = $54\frac{1}{54}$