#### Question

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

4

3

-2

3.5

#### Solution

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

Is there an error in this question or solution?

#### APPEARS IN

Solution The Value of √ 6 + √ 6 + √ 6 + . . . . is Concept: Solutions of Quadratic Equations by Completing the Square.