Question

Find the value of x if 
\sqrt{x + \sqrt{x + \sqrt{x + ........ \infty } } }x+x+x+........∞​​​ = 2010​

Answer 1

Required Answer:-

Given:

$\rm \sqrt{x + \sqrt{x + \sqrt{x + ... \infty } } } = 2010$

To find:

• The value of x.

Solution:

Given that,

$\rm \sqrt{x + \sqrt{x + \sqrt{x + ... \infty } } } = 2010$

Squaring both sides, we get,

$\rm \implies x + \sqrt{x + \sqrt{x + ... \infty } } ={ 2010}^{2}$

As said earlier that,

$\rm \sqrt{x + \sqrt{x + \sqrt{x + ... \infty } } } = 2010$

So,

$\rm \implies x + 2010 ={ 2010}^{2}$

$\rm \implies x = { 2010}^{2} - 2010$

$\rm \implies x = { 2010}^{2} - 2010$

$\rm \implies x =4,038,090$

Hence, the value of x is 4,038,090

Answer:

• The value of x is 4,038,090.

Answer 2

Answer:

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