Question

solve : root 2+root 2-root 2+root 2-x=x

Answer 1

Answer:

2

Step-by-step explanation:

Given problem,

\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+.....................\infty }}}}

Let,

\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+.....................\infty }}}}=x

\sqrt{2+x}=x

2+x=x^2

\implies x^2 - x - 2 =0

x^2 - 2x + x - 2=0

x(x-2)+1(x-2)=0

(x+1)(x-2)=0

⇒ x = - 1  or x = 2,

x = - 1  is not possible, because value of square root of a number can not be negative,

\implies \sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+.....................\infty }}}} = 2