`sqrt(2+sqrt(2+sqrt(2+……….)))` के बराबर है?

Options

A. `sqrt(2)`
B. `2sqrt(2)`
C. `2`
D. `3`

Answer

C

Explanation

`x=sqrt(2+sqrt(2+sqrt(2+)))`…………..
`x^(2)=2+sqrt(2+sqrt(2+))…………`
`x^(2)=2+x`
`x^(2)-x-2=0`
`x^(2)-2x+x-2=0`
`x(x-2)+1(x-2)=0`
`(x+1)(x-2)=0`
`x=2`
Shortcut method
When the question is inthis form i.e. `sqrt(x+sqrt(x+sqrt(x)))................`
Then factor the

So n1 is answer