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The Value of √ 6 + √ 6 + √ 6 + . . . . is - CBSE Class 10 - Mathematics

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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?

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