Question

the v
alue of x=√12+√12+√12+.... infinity, t​

Answer 1

Step-by-step explanation:

x=√12+√12+√12 infinity

do both side squares

Answer 2

Answer:

Step-by-step explanation:

There is a really interesting math trick behind it.

If you see a question like this take out the number inside it (in this case is  

12 )

Take consecutive numbers such as:

n ( n + 1 ) = 12

Always remember that the answer is  

n + 1

This is true because if you let the infinite nested radical function = x then realise that x is also also under the first root sign as:

x = √ 12 + x

Then, squaring both sides:  

x 2 = 12 + x

Or:  

x 2 − x = 12

x ( x − 1 ) = 12

Now let  x  = n + 1

Then  n ( n + 1 ) = 12

With the answer to the infinite nested radical function (x) being equal to  

n + 1

If you solve it you get  

n = 3

and  

n + 1 = 4

So, The answer is  4

Practice problems:

1  ⇒   ⎷ 72 + √ 72 + √ 72 + √72 + √ 72

S o l u t i o n → 9  

2 ⇒ ⎷ 30 + √ 30 + √ 30 + √ 30 + √ 30

S o l u t i o n→ 6

And wait!!!