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alexd00d
Group Title
a+b+c=4
a^2+b^2+c^2=10
a^3+b^3+c^3=22
find the values of a, b ,and c
 2 years ago
 2 years ago
alexd00d Group Title
a+b+c=4 a^2+b^2+c^2=10 a^3+b^3+c^3=22 find the values of a, b ,and c
 2 years ago
 2 years ago

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alexd00d Group TitleBest ResponseYou've already chosen the best response.0
cubic polynominals
 2 years ago

liza2 Group TitleBest ResponseYou've already chosen the best response.0
I have no idea, I'm commenting so that I'll get a notification when someone solves this.
 2 years ago

alexd00d Group TitleBest ResponseYou've already chosen the best response.0
If someone gets this they are the smartest person I know!
 2 years ago

joemath314159 Group TitleBest ResponseYou've already chosen the best response.1
First note that:\[(a+b+c)^2=a^2+b^2+c^2+2(ab+ac+bc)\Longrightarrow \]\[4^2=10+2(ab+ac+bc)\Longrightarrow ab+ac+bc=3\]Also:\[(a+b+c)^3=a^3+b^3+c^3+3(a+b+c)(ab+ac+bc)3abc\Longrightarrow\]\[4^3=22+3(4)(3)3abc\Longrightarrow abc=2\]So your system is equivalent to: a+b+c=10 ab+ac+bc=3 abc=2 Solving this system is the same as solving the polynomial: \[x^310x^2+3x+2=0\]So the solutions to this polynomial are the solutions to your system.
 2 years ago

joemath314159 Group TitleBest ResponseYou've already chosen the best response.1
oh, mistype, thats why things were acting weird. Your system is equivalent to:\[a+b+c=4\]\[ab+ac+bc=3\]\[abc=2\]which gives the polynomial:\[x^34x+3x2=0\]which gives solutions \[a= 2, b=1\sqrt{2}, c=1+\sqrt{2}\]
 2 years ago

joemath314159 Group TitleBest ResponseYou've already chosen the best response.1
mistype again, +2 instead of 2 >.>
 2 years ago

alexd00d Group TitleBest ResponseYou've already chosen the best response.0
You must have had loads of practice to be as good as you are!
 2 years ago
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