Question

Sqrt(12 + Sqrt(12 + Sqrt(12+......)))=X Find X

Answer 1

Let x=Sqrt(12 + sqrt(12 + (sqrt(12 + .....infinity))) 
Thus x^2=12 + sqrt(12 + (sqrt(12 + .....infinity)) 
x^2-12=Sqrt(12 + sqrt(12 + (sqrt(12 + .....infinity)))=x 
so x^2-x-12=0 
(x-4)(x+3)=0 
x=4,-3

Answer 2

Answer:

4

Step-by-step explanation:

Firstly, (....) implies the presence of (....∞)  infinity

Squaring both sides

$x^{2} = 12 + \sqrt{12 + \sqrt{12 + \sqrt{12 + \sqrt{12...... \infty} } } }$

∴ x² = 12 + x         (As given in the question $x = \sqrt{12 + \sqrt{12 + \sqrt{12 + \sqrt{12......\infty} } } }$  )

 The above equation can be written as

⇒ x² - x - 12 = 0

  This is a quadratic equation and can be solved through several ways, one of them is the factorisation method i.e., by splitting the middle term

⇒ x² - 4x + 3x -12 = 0

⇒ x ( x - 4 ) + 3 ( x - 4 ) = 0

⇒ ( x - 4 ) ( x + 3) = 0

Putting the brackets one-by-one equal to 0

x - 4 = 0 ⇒ x = 4

x + 3 = 0 ⇒ x = -3

As x is not likely to be -3

∴ x = 4 ( in case both are present in the options)