Solve the following equations for x:

, where x > 0

Given:-

Take

We know that, Formula

Thus,

⇒

We know that, Formula

Thus,

⇒

⇒

⇒

We know that, Formula

Thus,

⇒

⇒

By rationalisation

⇒

⇒

⇒ (x+1)^{2} = (1+√3)^{2}

⇒ x+1 = ±(1+√3)

⇒ x +1 = 1+√3 or x +1 = –1–√3

⇒ x = √3 or x = –2 – √3

as given, x > 0

Therefore

x = √3

3