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TopicFor which integers x is sqrt[x+sqrt(x+8)] a positive integer?
Robot2600
12/01/22 10:57:10 PM
#55
lderivedx posted...
I liked this one.

Answer:

We set sqrt(x+sqrt(x+8)) = a, for a some positive integer. Squaring out the roots then collecting coefficients, we get the equation:

0 = x^2 - (2a^2+1)x+(a^4-8)

Using the quadratic formula we notice that since (2a^2+1) is odd, (2a^2+1)^2-4(a^4-8) must be a perfect square and odd. The latter simplifies to 4a^2+33, so we set it equal to the square of an odd integer 2k+1 to get:

4a^2+33=(2k+1)^2

Subtract the (2k+1)^2 over and factor using difference of squares to get

(2a+2k+1)(2a-2k-1)+33=0

The product there must be an either an (11 and a 3) or a (33 and a 1), where one of them is negative. Solving this, the only positive solution to the former that works is when a=2 and a=8 for the latter. Going back to the polynomial in x^2, we solve and we get four solutions for x: 1, 8, 56, and 73. These are not guaranteed to solve the original equation, but all solutions to the equation are in that list, so you can check that the solutions are 1 and 56.

sick

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Topicif the universe is a holographic projection of a 2d surface
Robot2600
12/01/22 10:54:21 PM
#3
Questionmarktarius posted...
It's all an extrapolation of a single point.

i wasnt even gonna go there but goddamn, yea, maybe.

i dont think so tho, we need at least one dimension, just like we need at least 2 states (0 and 1) to convey information at all. but we dont need any more than that.

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TopicFor which integers x is sqrt[x+sqrt(x+8)] a positive integer?
Robot2600
12/01/22 10:52:14 PM
#53
you know what i meant, the ones cantor talked about.

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Topicif the universe is a holographic projection of a 2d surface
Robot2600
12/01/22 10:46:22 PM
#1
could that 2d surface be a projection of a 1d line? asking for a friend.

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TopicFor which integers x is sqrt[x+sqrt(x+8)] a positive integer?
Robot2600
12/01/22 10:44:21 PM
#50
Tyranthraxus posted...
Irrationals are real.

so they are! look at that everyone was wrong but now we know.

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TopicFor which integers x is sqrt[x+sqrt(x+8)] a positive integer?
Robot2600
12/01/22 10:41:23 PM
#47
surreals are actually real numbers

complex(imaginary), irrational, and transcendental numbers are not

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TopicFor which integers x is sqrt[x+sqrt(x+8)] a positive integer?
Robot2600
12/01/22 10:27:54 PM
#44
Vokrent posted...
There's numbers that aren't real?

yea bruh, imaginary (make no mistake they are VERY real)

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Topichaven't bowled in 15 years and then i did
Robot2600
12/01/22 10:26:34 PM
#1
125

im pumped! i bowled as a kid, and got pretty good at it. now i wanna get good again.

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TopicElon Musk...do you think he agrees with Kanye?
Robot2600
12/01/22 10:11:35 PM
#16
[LFAQs-redacted-quote]



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TopicFor which integers x is sqrt[x+sqrt(x+8)] a positive integer?
Robot2600
12/01/22 7:32:26 PM
#38
Showing that the number do go to infinity is a proof, from what I've seen on numberphile.

Hmmm, if we replace the 8 with a 7, is the answer 42? Yea I think so. So that's why it's like that, you square the number and the. Subtract the number and that's the only thing that fits?

10 should be 90... Yup.

The 1 working was a fluke then? Seems so.

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TopicFor which integers x is sqrt[x+sqrt(x+8)] a positive integer?
Robot2600
12/01/22 6:08:32 PM
#31
you can think about it and realize there is nothing else that will work because it's a very specific request. 64 is 2x2x2x2x2x2 so you can try other numbers like 512 and 4096 and realize it's probably not gonna work.

the top-level squareroot function means the answer is going to need a square of an integer, and that quickly goes to infinity that the +8 is too small to do anything, you'll always get an irrational squareroot because of that. squares aren't distributed like primes: 4, 9, 16, 25, 36, etc.... it always gets bigger and bigger to +8 will always fuck it up.

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TopicAnybody have any good bullet hell game rec's?
Robot2600
12/01/22 6:01:10 PM
#3
Ikaruga is the best.

then Mushihimesama

really why even play something that's not ikaruga.

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TopicCome to think of it, God probably doesn't even speak English.
Robot2600
12/01/22 5:59:56 PM
#4
if god's real then she's hotter and cooler than you. she does more drugs than you. she could beat your ass in call of duty. she could program better shit than call of duty if she werent too busy getting high and driving fast. the only person almost cool enough to hang out with is fucking satan.

and that's IF christianity is real so literally why even care.

also they ripped the entire christianity thing from egypt.

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TopicThe bread girl
Robot2600
12/01/22 5:57:19 PM
#5
was expecting the wonderbread girl

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Topicdo you hear it?
Robot2600
12/01/22 4:47:13 PM
#5
this topic is about pvp competition. who amoungst ye thrives on battle?

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Topicdo you hear it?
Robot2600
12/01/22 4:43:26 PM
#4
*dances*

https://youtu.be/mOQTYnGyweE

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Topicdo you hear it?
Robot2600
12/01/22 4:42:02 PM
#2
i didn't think so.

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TopicJust hit the gym again
Robot2600
12/01/22 4:41:33 PM
#2
good job

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TopicKanye is black Nazi now. (not a joke)
Robot2600
12/01/22 4:40:10 PM
#27
same, tc, same

fellsbadman

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TopicKanye loves Hitler because of microphones
Robot2600
12/01/22 4:37:43 PM
#31
"black skinhead" was not a metaphor

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TopicWhy do women like flowers so much?
Robot2600
12/01/22 4:35:49 PM
#8
lww99 posted...
this is why I dont buy them often at all, especially from a boutique. Im not paying $70 for a dozen roses that will die in a week or less.

yea id never buy flowers that's dumb. i like to paint flowers (i.e. on a canvas).

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TopicDarkRoast is a Mess 2: Femme Fatale
Robot2600
12/01/22 4:31:23 PM
#91
DarkRoast posted...
Yeah good idea I'll do that now.

It's weird. A bittersweet feeling. A month ago I would've been repulsed. Guy me hates it, girl me thinks I'm beautiful.

guys are dumb trust your girl

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TopicWhy do women like flowers so much?
Robot2600
12/01/22 4:29:33 PM
#2
i like them because they die, thus prompting me to meditate on life, death, and the inevitable disintegration of everything around me

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TopicSupreme Court keeps student loan relief program blocked, arguments set for Feb.
Robot2600
12/01/22 4:27:04 PM
#6
such fucking 1984 bullshit.... so those jackasses think they deserve MORE money, but because they didn't get enough then EVERYONE should get ZERO money because...

ya know what im just gonna:

*closes eyes*

*opens mouth*

*releases the SCREAMING BEES*

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Topicdo you hear it?
Robot2600
12/01/22 4:24:40 PM
#1
the cry of the warrior.

do you?

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TopicYou've supremely pissed off this character. How fucked are you? (Seconds game.)
Robot2600
12/01/22 4:17:50 PM
#4
lets'aagooooo

aww fuck i dead. Lion-O... i cant beat him in a fight!

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TopicSupreme Court keeps student loan relief program blocked, arguments set for Feb.
Robot2600
12/01/22 4:16:57 PM
#3
COVxy posted...
The wild thing about this shit is that the people who are trying to block this have no skin in the game. It's literally just vindictiveness.

that's why the federal judge gave it the go-ahead. these people are not injured because someone else gets free college. the end.

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TopicHelicopters against the moonlight... Our holy mother of the, Midnight
Robot2600
12/01/22 4:08:31 PM
#4
https://www.youtube.com/watch?v=msYtJGQ69sw

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TopicOn this day 40 years ago: Sharon B makes a prediction about video games
Robot2600
12/01/22 4:06:54 PM
#3
DeadBankerDream posted...
She's a word processor? Isn't that a computer program?

She means she types stuff up.

Well Sharon B, looks like you were on the wrong side of history.

edit: then i saw the date. SHARON B CAN SEE THE FUTURE

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TopicThe Kanye subreddit is having a moment
Robot2600
12/01/22 3:53:58 PM
#21
Clothes the sub.

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TopicThe Kanye subreddit is having a moment
Robot2600
12/01/22 3:39:23 PM
#10
Close the sub.

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TopicElon Musk VS Jeffery Bezos in a fist fight no rules
Robot2600
12/01/22 3:35:12 PM
#12
bezos and it's not even close

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TopicJesse James pregnant wife Porn Star Bonnie Rotten accuses him of cheating on her
Robot2600
12/01/22 3:33:49 PM
#4
i think i will not google this one

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TopicPokemon Scarlet/Violet patch coming tomorrow.
Robot2600
12/01/22 7:42:15 AM
#14
Dreepapult posted...
Lol I wonder what the timeline is for the performance patch

2022 ignore the problem
2023 ignore the problem
2024 new pokemon game, also has the framerate problem
2025 new switch, games run on it tho
2026 switch servers shut down

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TopicWould anyone be down for low-stakes CE poker?
Robot2600
12/01/22 12:43:24 AM
#2
mods! i need a mods!

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TopicJust when I finally found an app that lets me browse Twitter without an account
Robot2600
12/01/22 12:42:53 AM
#9
he means a home business

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TopicAre modern pro skateboarders better than Tony Hawk?
Robot2600
12/01/22 12:41:17 AM
#6
Complete_Idi0t posted...
One day someone will pull off the 901

some kid did a 1080 but not on a half-pipe.

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TopicPokemon Scarlet/Violet patch coming tomorrow.
Robot2600
12/01/22 12:23:59 AM
#3
WingsOfGood posted...
Removing dupe glitch?

you can bet on it. they dont even like to draw attention to it's existence.

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TopicThis universe is mine. I am GOD here!
Robot2600
12/01/22 12:23:07 AM
#2
as God intended

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TopicNZ parents refuse use of 'vaccinated blood' in life-saving surgery on baby
Robot2600
12/01/22 12:22:29 AM
#21
Narkansas

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TopicCE. You mind answer an easy math problem for me?
Robot2600
12/01/22 12:21:27 AM
#14
Tyranthraxus posted...
Chances are, however, the developers were mistaken when they said they were multiplicative. More likely there's some CDR constant and those percentages multiply against that constant.

yea. my thoughts were that the bonuses "stacked" and didn't "multiply"

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TopicCE. You mind answer an easy math problem for me?
Robot2600
12/01/22 12:20:07 AM
#13
Robot2600 posted...
it's 400% multiplied

actually the order they are applied matters if it's a debuff. if it's a debuff you should hit the 200% first and then the 100%

1 min -> 3 min -> 6 min
vs
1 min -> 2 min -> 4 min

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TopicCE. You mind answer an easy math problem for me?
Robot2600
12/01/22 12:18:25 AM
#12
DepreceV2 posted...
Ah! That makes sense! I should have converted it that way. What if it was two debuffs. One is 100% longer and the other is 200%?

it's 400% multiplied

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TopicCE. You mind answer an easy math problem for me?
Robot2600
12/01/22 12:02:48 AM
#6
they mean 100% is actually 50% and 200% is actually 25% (of original time)

50% faster of 25% total time would put it at 12.5% the original time, this is probably what the devs mean if it's truly multiplicative.

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TopicDoes your phone raw dog the world?
Robot2600
11/30/22 11:50:05 PM
#11
ToucheTurtle posted...
I've never used a case of screen protector on any phone I've owned.

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TopicRolled my van off a 20 foot berm going to work today.
Robot2600
11/30/22 11:48:28 PM
#14
it sounds like the car still works? obviously doesnt look as nice anymore

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TopicRolled my van off a 20 foot berm going to work today.
Robot2600
11/30/22 11:43:02 PM
#12
posting in legendary topic

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TopicYour reaction when you see a CEuser who you dislike having a bad day/time?
Robot2600
11/30/22 10:56:47 PM
#7
o_o

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TopicAlexa vs Google Home vs Apple Home?
Robot2600
11/30/22 10:55:41 PM
#7
pass.

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