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

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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

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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cubic polynominals
I have no idea, I'm commenting so that I'll get a notification when someone solves this.
If someone gets this they are the smartest person I know!

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Other answers:

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: \[x^3-10x^2+3x+2=0\]So the solutions to this polynomial are the solutions to your system.
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:\[x^3-4x+3x-2=0\]which gives solutions \[a= 2, b=1-\sqrt{2}, c=1+\sqrt{2}\]
mistype again, +2 instead of -2 >.>
You must have had loads of practice to be as good as you are!

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