I checked wolfram alpha and the answer is ||5|| but I have no clue on how to solve it
#Square roots in cube roots
rugged nimbus
gray blazeBOT
I checked wolfram alpha and the answer is ||5|| but I have no clue on how to sol...
- Ask your question and show the work you've done so far. If you've posted a screenshot of a question, specify which part you need help with.
- Wait patiently for a helper to come along.
- Once someone helps you, say thank you and close the thread with:
+close - Feel free to nominate the person for helper of the week in #helper-nominations
- Do not ping the mods, unless someone is breaking the rules. If there is a conflict amongst multiple helpers feel free to ping “Helper Mod”
- If you're happy with the help you got here, and the server overall, you can contribute financially as well:
dull rune
If you were just given this expression, then computing it would be really cumbersome (basically: you would need to compute the minimal polynomial of a using resultants)
dull rune
however, here, you are given that a is an integer
so, I think that you are just expected to show that 4 < a < 6
rugged nimbus
i'll try
dull rune
(it seems annoying tho, but I see no easier way)
dull rune
yeah, maybe with a more precise error in place of ~ (like ±0.1) just to be sure if you're required to justify your answer
rugged nimbus
alright then, tysm!
dull rune
you're welcome
rugged nimbus
would you mind if i ask another question of the same thing? theres one more thing im still curious with
dull rune
sure
rugged nimbus
i stumbled into an answer using wolfram alpha so it appears that it could be simplified more; i just don't know how i would write so that it would be reasonable. i'd assume that it's related to the minimal polynomial too?
dull rune
I don't really understand the sequence of equalities, what is equal to what
dull rune
ok, if you see this then good job (you also need to perform a similar trick for the second square root)
but it requires to guess the solution
rugged nimbus
ok, if you see this then good job (you also need to perform a similar trick for ...
i checked the second one,, it seems to cancel each other then it gets 5
dull rune
ok
so either you guess these simplifications (there's no general method to see it), either you know it is an integer and then you just perform a precise enough approximation, either you use the general method of computing the minimal polynomial (but don't do it by hand here…)
rugged nimbus
alright then 🥹 tysm!!
dull rune
you're welcome
pearl pathBOT
Unable to parse the channel name
final sky
square root of 4 -31 is not possible
final sky
square root of 4 -31 is not possible
fortunately, that doesn’t appear in this question
wheat wagon
square root of 4 -31 is not possible
$\int_{-\infty}^{\infty} e^{-x^2} dx$ find a closed form of this
supple glacierBOT
;( | 追放された興奮
rugged nimbus
uhh i managed to find a way to simplify $20sqrt[3]{4}-31$
supple glacierBOT
NatTaylorsV
rugged nimbus
$20\sqrt[3]{4}-31 \ = 20\cdot{2^\frac{2}{3}}-32+1 \ = 16\cdot{2^\frac{2}{3}}+4\cdot{2^\frac{2}{3}}-32+1$ \ Let $b = 2\cdot{2^\frac{2}{3}}, {b^3=4}$ \ $= 16b+4b-32+1 \ = 4b^4-8b^3 +4b+1 \ = (2b^2-2b-1)^2$
supple glacierBOT
NatTaylorsV
rugged nimbus
the problem is i have to simplify $20\sqrt[3]{16}-16$ to $(2b^2-2b+4)^2$ so that it cancels out and get 5 but i'm not sure how
supple glacierBOT
NatTaylorsV
final sky
why not just square (2b^2 - 2b + 4) and see what you end up with?
rugged nimbus
i got 4b^4-8b^3-20b^2-16b+16, then i got stuck afterwards lol
rugged nimbus
upd: i got this but still dont quite understand. is there a way to complete the square (i.e. quartic to squared quadratic)?
rugged nimbus
still dont understand why
rugged nimbus
+close