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

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379 sats \ 9 comments \ @south_korea_ln 19 Dec science

Solve

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

300 sats \ 2 replies \ @CruncherDefi 19 Dec

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.

0 sats \ 1 reply \ @south_korea_ln OP 19 Dec

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

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

0 sats \ 0 replies \ @south_korea_ln OP 20 Dec

For the record,

and

are two roots. The last two roots can easily be found from the remaining quadratic equation.

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

which is in contradiction with the initial root problem, so both can be discarded too. Only

is a valid solution to the initial problem.

137 sats \ 1 reply \ @SimpleStacker 19 Dec

Here's a hint:

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

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

30 sats \ 0 replies \ @south_korea_ln OP 19 Dec

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~~

100 sats \ 3 replies \ @Scroogey 19 Dec

You should have used 1807 instead of 7 😉

100 sats \ 2 replies \ @south_korea_ln OP 19 Dec

@Aardvark can likely solve that one ;)

300 sats \ 1 reply \ @Aardvark 19 Dec

OMG it's 42!!!!

11 sats \ 0 replies \ @south_korea_ln OP 19 Dec

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~~