Find all positive integers (x,y) that satisfy y=√(x+x√x)
Find all positive integers (x,y) that satisfy y=√(x+x√(x+x√x))
Nice puzzle.
Checking small values gives
y=√((x^2-1)^2+(x^2-1)^2(x^2-1)) replacing x in the original formula with (x^2-1)^2; and
y=√((2x-1)^2-1)^2+(2x-1)^2-1)^2√((2x-1)^2-1)^2+(2x-1)^2-1)^2√(2x-1)^2-1)^2)) replacing x in the original formula with ((2x-1)^2-1)^2
for x=1,2,3,...,
Presumably the format can be extended to more complex radicals.
Now corrected.
Edited on June 4, 2022, 9:14 am
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Posted by broll
on 2022-06-04 08:33:19 |
Possible Solution
