SOLUTION: X=sqrt(4+sqrt(4-sqrt(4+sqrt(4-.........upto infinity. find x.

Algebra ->  Systems-of-equations -> SOLUTION: X=sqrt(4+sqrt(4-sqrt(4+sqrt(4-.........upto infinity. find x.      Log On


   

Question 60418: X=sqrt(4+sqrt(4-sqrt(4+sqrt(4-.........upto infinity.
find x.
Answer by joyofmath(189) About Me  (Show Source):
You can put this solution on YOUR website!
x=sqrt(4+sqrt(4-sqrt(4+sqrt(4-...
x=sqrt%284%2Bsqrt%284-x%29%29+
Then, x%5E2=4%2Bsqrt%284-x%29
Or, x%5E2-4=sqrt%284-x%29
Or, %28x%5E2-4%29%5E2=4-x
Or, %28x%5E2-4%29%5E2%2Bx-4=0
Or, x%5E4-8x%5E2%2Bx%2B12+=+0
This is a 4th degree, or quartic, polynomial.
There's a quartic equation solver here: http://www.1728.com/quartic.htm

Plug in 1, 0, -8, 1, and 12 as values for A, B, C, D, E. The value for X2 (2.3027756477...) is correct in that that value of x satisfies the equation: x=sqrt%284%2Bsqrt%284-x%29%29 and the sum looks like it's a bit bigger then 2.