Question

If x = 9 + 4√5 , then find the value of √x – (1/√x)

Answer 1

√x + 1/√x = √20

Explanation:

Given x = 9 + 4√5 -----(1)

Then 1/ x = 1 / (9 + 4√5) -----(2)

Multiplying both numerator and denominator by (9 – 4√5),

we get:

1/ x = (9 – 4√5) / [(9 +4√5) * (9 – 4√5)]

1/ x = (9 – 4√5) / (81 – 80) = (9 – 4√5) / 1 = (9 – 4√5)

(√x + 1/√x )^2 = x + 1/x + 2

Substituting values from equation 1 & 2, we get:

(√x + 1/√x )^2  = (9 + 4√5) + (9 – 4√5) + 2 = 9 + 9 + 2 = 20

(√x + 1/√x)^2 = 20

Therefore √x + 1/√x = √20 = 4.47