Question

x=5+root 3 then root x-1/root x=?​

Answer 1

Answer:

Step-by-step explanation:

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,

L.H.S = (√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 Or 2√3 = R.H.S