Question

The value of \[\sqrt{6 + \sqrt{6 + \sqrt{6 +}}} . . . .\] is 

 

Options

• 4

• 3

• -2

• 3.5

Answer 1

Let `x = sqrt(6 +sqrt(6+sqrt(6+sqrt(6+).....`

Squaring both sides we get

`x = sqrt(6 +sqrt(6+sqrt(6+sqrt(6+).....`

`x^2 = 6 + x`

`x^2 - x - 6 = 0`

    `x^2 = 3x + 2x - 6 = 0`

`x (x - 3) + 2(x - 3) = 0`

          `(x - 3)(x + 2) = 0`

(x - 3) = 0

       x = 3

 or

(x +2) = 0

 x = -2

The value of x cannot be negative.

Thus, the value of x = 3