Question

if
$x = 3 + \sqrt{2}$
then find
(1) x²+1/x²
(2) x⁴+1/x⁴




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Answer 1

Answer:

(1) x²+1/x² = 12/11

(2) x⁴+1/x⁴ = 86/85.

Step-by-step explanation:

Given,

x = 3 + √2

Now consider,

(1) x²+1/x²

= (3+√2)² + 1/(3+√2)²

= 9 + 2+1/9+2

= 12/11

:. x²+1/x² = 12/11.

(2) x⁴+1/x⁴

= (3+√2)⁴ + 1/(3+√2)⁴

= 81+4+1/81+4

= 86/85

:. x⁴+1/x⁴ = 86/85.