[Not-so-daily puzzle] Nested roots \ stacker news ~science

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Solve

Previous iteration: #807847 (solution in #809723) Nice puzzle by @SimpleStacker in #812338, too.

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.

You can use Polynomial long division to find the factors of this quartic equation...

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

You should have used 1807 instead of 7 😉

@Aardvark can likely solve that one ;)

OMG it's 42!!!!

Yes!!!

You've waited long and hard for this one, and then I missed the opportunity to choose this option. Luckily @Scroogey was there to catch the ball~~

Here's a hint:

shows up on the right hand side of the equation too...

Then you can do a simple guess and check...

Thanks for letting other people have their fun too. Good hint, this should help them.

This one is indeed likely a bit easy for you~~