For the record, $$2$$ and $$-3$$ are two roots. The last two roots can easily be found from the remaining quadratic equation. $$-3$$ can be discarded due to being a negative number whereas a root is always positive. As for the two roots from the quadratic equation, one is negative, whereas the other one is larger than $$\sqrt{7}$$ which is in contradiction with the initial root problem, so both can be discarded too. Only $$2$$ is a valid solution to the initial problem.

You can use [Polynomial long division](https://en.wikipedia.org/wiki/Polynomial_long_division) to find the factors of this quartic equation...

But guessing in this case works too, and is faster :)

south_korea_ln

science

[Not-so-daily puzzle] Nested roots

Saw the hint before trying to solve all by myself :((

```
k = sqrt(7-sqrt(7+k))
k^2 = 7-sqrt(7+k)
sqrt(7+k) = 7-k^2
7+k = (7-k^2)^2
7+k = 49 - 14k^2 + k^4
k^4 - 14k^2 - k + 42 = 0
```
You can probably solve it analytically, but I quickly guessed k=2 looking at the numbers.
