SOLUTION: sqrt(2+sqrt(2-sqrt(2+x))) =x 1/(1.2.3.0 +1/(4.5.6)+1/(7.8.9)+.....

Question 86183: sqrt(2+sqrt(2-sqrt(2+x))) =x

1/(1.2.3.0 +1/(4.5.6)+1/(7.8.9)+.....
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
sqrt(2+sqrt(2-sqrt(2+x))) =x
Square both sides to get:
2+sqrt(2-sqrt(2+x))=x^2
Rewrite:
sqrt(2-sqrt(2+x)) = x^2-2
Square both sides to get:
(2-sqrt(2+x)) = (x^2-2)^2
Rewrite:
-sqrt(2+x) = (x^2-2)^2-2
Square both sides to get:
2+x = [(x^2-2)^2-2]^2
2+x = [x^4-4x^2+2]^2
2+x = x^8-8x^6+24x^4-16x^2+4
x^8+8x^6+24x^4-16x^2-x+2 = 0
x=0.3583494...; x=0.687106...
==========
1/(1.2.3.0 +1/(4.5.6)+1/(7.8.9)+.....
Comment: What do you mean by 1/1.2.3.0 ???
--------------
Cheers,
Stan H.
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