Question

Please answer second and fifth bit

Answer 1

Answer:

(ii) 2-2√2 / 1-√2, (v) 18-12√2 / 17-12√2

Step-by-step explanation:

if x= 1-√2

then, x+1/x for (ii)

= (1-√2) - 1 / 1-√2

= (1-√2)² - 1 / (1-√2)

= 1+2-2√2-1 / 1-√2

= 2-2√2 / 1-√2 ans.

now, for (v), x⁴+1/x⁴

= (1-√2)+1/(1-√2)

= (1+2-2√2)² + 1 / (1+2-2√2)²

= (3-2√2)² + 1 / (3-2√2)²

= [(3-2√2)⁴ + 1] / (3-2√2)²

= [9+8-12√2+1] / (3-2√2)²

= [18-12√2] / 9+8-12√2

= [18-12√2] / [17-12√2] ans.

nice question✨