Question

If x= 9+4√5 then find the value of √x-1/√x

Answer 1

Given x = 9 + 4√5, find √x - 1 / √x

√x = √(9 + 4√5)

√x = √(√5 + √4 + 2√(5x4))

√x = √(√5 + √4)2

√x = √5 + 2

1 / √x = 1 / (√5 + 2) rationalize we get

1 / √x = (√5 - 2)

∴ √x - 1 / √x = √5 + 2 - √5 + 2 = 4.