Question

x=9+4 root5
Find the value of root x + 1/root x

Answer 1

Step-by-step explanation:

Given x = 9 + 4√5.

⇒ 4 + 5 + 2 * 2 * √5

⇒ (2)^2 + (√5)^2 + 2 * (2) * (√5)

It is in the form of a^2 + b^2 + 2ab = (a + b)^2.

⇒ (2 + √5)^2.

So, x = (2 + √5)^2.

Then, √x = (2 + √5).

Now,

Hence,

⇒ √x - (1/√x)

⇒ (2 + √5) - (√5 - 2)

⇒ 2 + √5 - √5 - 2

⇒ 4.

Therefore, the value of √x - (1/√x) = 4.

Hope this helps!