Question

The value of \[\sqrt{15-2\sqrt{15-2\sqrt{15-2\sqrt{15........}}}}\] is?

Answer 1

If this has a value, call that value x. Then
\[ x = \sqrt{15 - 2\sqrt{x}} \]
Solve that equation.

Answer 2

let
\[ y = \sqrt{15-2\sqrt{15-2\sqrt{15-2\sqrt{15........}}}} \]
square it
\[ y^2 = 15-2\sqrt{15-2\sqrt{15-2\sqrt{15........}}} \]

\[ y^2 = 15-2y \]
solve for y

Answer 3

oops yes,
\[ x = \sqrt{15-2x} \]

Answer 4

y=3 or y=-5

Answer 5

@experimentX then

Answer 6

is it 3 .....

Answer 7

sorry ... from JanesJ's method ... it's 3

Answer 8

you are not getting negative no from \( \sqrt{ ....}\)