You should be able to solve this.If x + 1/x = 5,find the value ofx^5 + 1/x^5.
what is the exact value pi
>>13006985
>>13006985uuuuuhhhhh 9?
I can barely add and subtract
is it 2525 lole
>>13007014Yay u did it!
>>1300698521
>>13006985Chiyo chan pls have mercy
good threade
>>13007014Could 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 = 23p_3 = 5·23 − 5 = 110p_4 = 5·110 − 23 = 527p_5 = 5·527 − 110 = 2525So 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
>>13008106Woah epic!
>>13007330lol
>>13006985good threade
>>13006985holy h*ck i love these threadsx + 1/x = 5x^2/x + 1/x = 5(x^2 + 1)/x = 5x^2 + 1 = 5xx^2 - 5x + 1 = 0apply the solving formulax = (5 +- sqrt(5^2 - 4*1*1)) / 2*1x = (5 + sqrt(21)) / 2 or (5 - sqrt(21)) / 2the solutionx^5 + 1/x^5 = 2525 (for both solutions)
>>13008285Not 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.
>>13006985But there's literally no way to solve the value of x in x + 1/x = 5So 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
>>13008362please kill yourself faggot
>>13008369Okay, 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
>>13008464what happens when u try to solve the equation if x = 4.791287847477is it ur contention that 4.791287847477 is an imaginary number
>>13008362how can math be real if numbers aren't real
>>13008489finally someone said itYour fortune: Very Bad Luck
>>13008489u can vibe it out with fake numbers it still works
>>13008464Well, 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.
>>13008507I guess I'm sorry for being wrong about the math question. I admit to that.
>>13008507But I still hate doremi posters for what they did to this board. Is all the bavi hate coming from doremi posters?
>>13008521The problem isn't that you were wrong in a maths question, and you know that. Stop trying to act innocent here.
>>13008524Maybe vent about it in your doremi thread?
>>13008522dubs poster>>13008524he is a pathological liar
>>13008522You know that's not true also. You invite hate from almost every group by acting the same way as you have in this thread. Among them, Doremi posters are probably the least likely to be hateful, but you are especially hateful to them. But, I think you're trying to shift focus here. This isn't about Doremi, this is about you.
>>13008652Fuck all doremi posters. Your boos mean nothing, I've seen what makes you cheer
>>13008665This was an opportunity for you to learn, but you're deflecting to Doremi. Are you going to start believing it's only Doremi posters who dislike you? This might be a new low for you
>>13008665Your continued existence only serves to grow the strength of the doremi cause.
