Deneb - 10 months ago 46

Python Question

I really don't know how to write this correctly. This is how I tried:

`def is_cardano_triplet(a, b, c):`

f = lambda x: x ** 1. / 2

g = lambda x: x ** 1. / 3

return g(a + b*f(c)) + g(a - b*f(c)) == 1

print is_cardano_triplet(2,1,5) # I should get True

I should get

`True`

`2, 1, 5`

Answer

Doing a bit of research ~~and calculations, solving the equation for the variable c~~, I found out that

and therefore

Now, due to floating point arithmetic being imprecise on binary-based systems for known reasons, the first formula is pretty hard to compute precisely. However, **the second one is much easier to compute** without floating point precision errors since that it doesn't involve irrational functions and `a`

, `b`

and `c`

are integers.

Here's the smart solution:

```
def is_cardano_triplet(a, b, c):
return (a + 1)**2 * (8*a - 1) - 27*b**2*c == 0
>>> is_cardano_triplet(2, 1, 5)
True
```