Question

if x =5+2root6 then, find the value of root x - 1/roo2t22 2x.

Answer 1

Answer:

x = 5 - 2√6

1/x = {1/(5 - 2√6)

⇒ 1/x = {1/(5 - 2√6)} × (5 + 2√6)/(5 + 2√6)

= (5 + 2√6)/25 - 24

= 5 + 2√6

Now,

(√x + 1/√x²) = x + 1/x + 2 × √x × 1/√x 

= x + 1/x + 2

⇒ √x + 1/√x = √x + 1/x + 2 (whole root)

= √5 - 2√6 + 5 + 2√6 + 2

= √5 + 5 + 2

= √12..