Using Vieta's Formulas on a Cubic Equation

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[SyberMath]

Sorry, I forgot to PREMIERE this video! 😂😂😂
I hope you enjoyed both methods. Vieta's Formulas are fun and super useful!
And the proof is fairly easy. Was this a hard problem? An easy problem? What do you think? Please let me know here ⬇
He is one of my newest members! Thank you, Roh4n, for the support!

[notfancy]

And this is true for *all* depressed cubics! The example cubic was a red herring all along..

[aashsyed]

Your channel is growing fast!!! I like your video happy birthday 2 u

[armacham]

I love that there's such a simple way to solve the problem. It reminds us to keep our eyes open and look for different ways to approach the problem. Instead of assuming that every problem will be a grind. Not that grinding is a bad thing. It's good to have variety.

[utuberaj]

Really great. The 2nd method was genius!

[aashsyed]

I like your channel so much! I hope your channel is growing

[snejpu]

Luckily I spotted the 2nd method first, so it took me less time. I was even wondering if there was some mistake here. : ) But not.

[MathElite]

Ooh a cubic equation question! I have some knowledge now on this subject lol
nice video and wow that result is super nice!
I love the 2nd method wow

[aashsyed]

You are so awesome 😎😎😎 your channel is growing fast!!!! I like your

[math]

watching and learning bro, fantastic job

[arundhatimukherjee]

One thing is interesting. The expression in the problem is always equal to -3, whatever may be the coefficients of x¹ and x⁰(or constant term), provided 0 is not a root.

[rio.xyz_]

Wow...second method is amazing and very simple 👏👏

[titassamanta]

I added 1 to each term of the expression whose value was to be found and then subtracted 3. So we we get (m+n+k)× something - 3=0×that 'something- 3= -3

[tarunmnair]

Nice video, but slightly lengthy approach...
WKT, m+n+k = 0 (blessing in disguise, needed only this equation)
=> m+n = -k ; n+k = -m ; k+m = -n.
Thus, m/(n+k) + n/(k+m) + k/(m+n) = m/(-m) + n/(-n) + k/(-k) = -1 -1 -1 = -3.

[MushookieMan]

Is it possible to solve one of these rational expressions in terms of roots if it isn't symmetric? Is there a definition like m>n>k or something?

[rcnayak_]

Therefore, in this cubic equation, the coefficients 99, 77 do not matter and can assume any values as long as the coefficient of x² is 0, so that m + n + k = 0. And we go straight putting m + n = - k, m + k = - n and n + k = - m in the problem to get - 3 instantly.

[aashsyed]

You are awesome your channel is growing fast

[ashishpradhan]

Ahh! I don't supposed to miss the premier today!

[haneyred]

Looks like the device seems to be tired of the hard way 😄 8:38

[nickruffmath]

This requires 0 to not be a root but it obviously isn't because of the nonzero constant term. Great approach for a depressed cubic...which every cubic can be converted into through a linear change of variables from x to x - b/(3a)