Question

x+✓(x+✓(x+✓(x...)))=2 find x

Answer 1

here is the answer hope this is helpful to you

Answer 2

Value of $\bf x = 2 - \sqrt{2}$

Given:

• $x + \sqrt{(x + \sqrt{(x + \sqrt{(x + ...)}) }) } = 2$

To find:

• Find the value of x.

Solution:

Concept to be used:

• The infinite series have value 2.
• Taking something from infinity leaves infinity. i.e. (∞ -a)= ∞, where a is some small quantity.

Step 1:

Take x to RHS

$\sqrt{(x + \sqrt{(x + \sqrt{(x + ...)}) }) } = 2 - x...eq1$

as the value of complete sequence is 2;and we just remove one value, and this sequence ends on infinity.

Step 2:

Put the value from eq1

$\sqrt{(x + \red{ \sqrt{(x + \sqrt{(x + ...)}) }) }} = 2 - x$

Thus,

Put the value of series in LHS

$\sqrt{x+\red{2-x}} = 2 - x$

or

$\sqrt{2} = 2 - x$

or

$x = 2 - \sqrt{2}$

Thus,

Value of $\bf x = 2 - \sqrt{2}$

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