Question

√12+√12+√12+√12 to infinity

Answer 1

the question should be like in the figure

x=  √12+x
x²=12+x
x²-x-12=0
x=3

Answer 2

The value of $\sqrt{12+\sqrt{12+\sqrt{12+....infinite }}$  is "4".

Step-by-step explanation:

We have,

$\sqrt{12+\sqrt{12+\sqrt{12+....infinite }}$     ....(1)

Let$y = \sqrt{12+\sqrt{12+\sqrt{12+....infinite }}$

Now, equation (1) becomes, we get

$Let y = \sqrt{12+y }}$

Squaring both sides, we get

$y^{2} =12+y$

⇒ $y^{2} -y-12=0$

⇒$y^{2} -4y+3y-12=0$

⇒ $(y-4)(y+3)=0$

⇒$y-4 = 0$ or $y+3 = 0$

⇒ y = 4 or y = -3 [∵ negative value is neglected]

∴ y = 4

Hence, the value of $\sqrt{12+\sqrt{12+\sqrt{12+....infinite }}$  is 4.