Question: Solving equation with radicals

January 04 2013 VolMike 20


Good day, dear Friends!

I'm trying to find real positive roots  of equation 

sqrt(x+3-4*sqrt(x-1))+sqrt(x+8-6*sqrt(x-1)) = 1 with Maple 16.01.

One can easly verifies that this euqation has at least two positive  real (integer) solutions: at x=5 and x=10,

but Maple function solve(sqrt(x+3-4*sqrt(x-1))+sqrt(x+8-6*sqrt(x-1)) = 1, x) assuming x::positive; returns nothing but x. Is it possible to solve that equation by Maple's internal functions?



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