Question

$\sqrt{2 - \sqrt{2 - \sqrt{2 - \sqrt{2 - .......} } } }$
=?¿

Answer 1

Consider whole equation as x.

So, you can see that

x = √(2 - x)

x² = 2 - x

x² + x - 2 = 0

x² + 2x - x - 2 = 0

x(x + 2) - 1(x + 2) = 0

(x + 2)(x - 1) = 0

So, x = -2, 1.

But square root can't have negative value.

So, its answer is 1.



Thank you.