Solve
Previous iteration: #807847 (solution in #809723)
Nice puzzle by @SimpleStacker in #812338, too.
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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 = 0You 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 :)
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 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 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: k 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~~