Question

if X=3+2√2, find the value of (√x - 1/√x)​

Answer 1

Answer:

2. GQ

Step-by-step explanation:

x = 3 + 2√2

1/x = 1/(3+ 2√2)* (3-2√2)/(3-2√2)

= 3- 2√2

using identity (a-b)^2 = a^2 + b^2 - 2ab

=> (a - b) = √(a^2+b^2-2ab)

√x - 1/√x =√{ (√x)^2 + (1/√x)^2 - 2(√x)(1/√x) }

√x - 1/√x = √{(x + 1/x) - 2 }

= √(3+2√2 +3 - 2√2 - 2) = √4 = 2