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Losing Digits


Hi,

I'm chasing for a lot of Digits in my mathematica computation.
Unfortunately, I started mathematica two days ago and I do not
understand every behaviour yet.
Now, to the problem. I set Ndigits to 200 and using the N
function for declaring some variables to be very accurate.
But after

t=Max[Cases[t./Solve[(p[[1]]+t*v[[1]])^4+(p[[2]]+t*v[[2]])^4==1,t],_?Positive]];


I lost  almost all of the 200. How I can force this equation to
be very accurate?

Thank you for your help.

Regards,
Martin


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