A Nice Radical Expression

[@farhansadik5423]

I'm very thankful for the Cardano's method tutorial! I was struggling to understand it but this video really cleared that up for me!

[@rob876]

x^3 = 6 + x
x^3 - x - 6 = 0
x = 2

[@joeeeee8738]

x^3 = 6 + x
x^3 - x = 6
x (x^2 - 1) = 6
x (x+1)(x-1) = 6
(x-1) x (x+1) = 6 --> 3 consecutive numbers
6 can be decomposed onto 2 * 3 and also to 1 * 2 * 3 trivially
x = 2 is a valid solution

[@lastchance8142]

If this was on the MIT entrance exam, I would not be gettimg into MIT.

[@holyshit922]

I can see recursion here
so let's define recursive sequence and calculate the limit

[@mathswan1607]

2