[s4s] Tribune

what is the exact value pi >>13006985 >>13006985
uuuuuhhhhh 9? I can barely add and subtract is it 2525 lole >>13007014
Yay u did it! >>13006985
21 >>13006985
Chiyo chan pls have mercy good threade >>13007014

Could you prove it to us? Why is it 2525? >>13006985
*rapes Chiyo-chan* The answer is 2525. The anon guessing 9 is way off.

The clean way uses power sums. Let p_n = x^n + 1/x^n. There's a recurrence: p_n = (x + 1/x)·p_{n-1} − p_{n-2} = 5·p_{n-1} − p_{n-2}.

Starting from p_1 = 5:
p_2 = 52 − 2 = 23
p_3 = 5·23 − 5 = 110
p_4 = 5·110 − 23 = 527
p_5 = 5·527 − 110 = 2525
So x5 + 1/x5 = 2525.

(Note it works even though x itself is irrational — x = (5 ± √21)/2 — because the symmetric combination always lands on an integer.)

And Yuji Sakai asking for "the exact value pi" is just shitposting; π has nothing to do with this one. This is how I worked it out. I had to use the quadratic formula, I didn't understand the recurrence solution which is probably more elegant >>13006985 >>13008106
Woah epic! >>13007330
lol >>13006985
good threade >>13006985
holy h*ck i love these threads

x + 1/x = 5
x^2/x + 1/x = 5
(x^2 + 1)/x = 5
x^2 + 1 = 5x
x^2 - 5x + 1 = 0

apply the solving formula
x = (5 +- sqrt(5^2 - 4*1*1)) / 2*1
x = (5 + sqrt(21)) / 2 or (5 - sqrt(21)) / 2

the solution
x^5 + 1/x^5 = 2525 (for both solutions) >>13008285
Not bad, but you introduced a small inaccuracy when you limited the number of significant figures midway through your process. The difference between the real number and your rounded 0.21 is only a 0.6% change, but when the next step involves an exponent of 5, that difference has a large effect.
When dealing with irrational numbers, I recommend using ANS on your calculator, instead of manually inputting it, it will preserve the precision.
I also noticed that you try to be consistent in keeping your numbers to two decimal places. But when it comes to precision, the number of decimal places does not matter as much as the number of significant figures. Your intermediate step answer was 0.21, and your final answer was 2448.52. These are both 2 decimal places, but one has 2 significant figures, and the other has 6 significant figures. Once you drop significant figures, you can't add them back, because you have lost that precision. >>13006985
But there's literally no way to solve the value of x in
x + 1/x = 5
So what does any of this even mean? I never understood what math accomplishes when you start using made-up imaginary numbers that aren't actually real >>13008362 >>13008362
please kill yourself faggot >>13008369
Okay, since I'm autistic, can you break down what was so bad about what I just posted that you need to post this kind of reaction. Obviously I said something that upsets you, but I don't know what, and I genuinely want to know what it is so I can be a better poster for this board >>13008464
what happens when u try to solve the equation if x = 4.791287847477
is it ur contention that 4.791287847477 is an imaginary number >>13008362
how can math be real if numbers aren't real >>13008489
finally someone said it

Your fortune: Very Bad Luck >>13008489
u can vibe it out with fake numbers it still works >>13008464
Well, you said something confidently incorrect. There IS a way to solve for x, and it doesn't involve imaginary numbers. Then, in your frustration, you blamed math rather than yourself, which looks pathetic to anyone who likes mathematics, which is exactly who this thread was made for (it clearly wasn't intended for you, yet you waltzed in here anyway).
You see, ignorance alone isn't bad, I don't even hate dumb people, but in this case it's you, who makes sure to enter every thread to impart what you think is wisdom, and you aggressively double down or deflect when you are wrong. See, you're not only dumb, you're arrogant and rude and opinionated. This is the Doremi hater, revealed for all he is worth. >>13008507
I guess I'm sorry for being wrong about the math question. I admit to that. >>13008507
But I still hate doremi posters for what they did to this board.
Is all the bavi hate coming from doremi posters? >>13008521
The problem isn't that you were wrong in a maths question, and you know that. Stop trying to act innocent here. >>13008524
Maybe vent about it in your doremi thread? >>13008522
dubs poster
>>13008524
he is a pathological liar