Question

three variable are missing a+b+c=0, a²+b²+c²=3, and a⁴+b⁴+c⁴=? And a^5+b^5+c^5=10

Answer 1

If you want integers, then clearly
a,b,c = ±1, since the squares are all positive and add to 3.
But then a+b+c ≠ 1

So, now we need to check real values.
c = -(a+b), so
a^2 + b^2 + (a+b)^2 = 3
2a^2 + 2ab + 2b^2 = 3
a = ±√2, b = ∓1/√2
so, c = ±(√2 - 1/√2)
But now a^5+b^5+c^5 ≠ 10

So now we are left with some complex values. wolframalpha comes up with some, but somehow I don't think that's what you want:

https://www.wolframalpha.com/input/?i=solve+a%2Bb%2Bc%3D0%2C+a%C2%B2%2Bb%C2%B2%2Bc%C2%B2%3D3%2C++a%5E5%2Bb%5E5%2Bc%5E5%3D10

Answer 2

Yes sir ..........

Can you give the identities of

a²+b²+c²=? ,a⁴+b⁴+c⁴=? And a^5+b^5+c^5=?

Thanks Obleck

Answer 3

Master obleck the original question is
a+b+c=0
a³+b³+c³=3
a⁴+b⁴+c⁴=?
a^5+b^5+c^5=10

Sorry for the typo

Answer 4

makes a big difference.
Using my prior steps, I get one solution as
a = -1
b = (1-√5)/2
c = (1+√5)/2
Now surely you can find a^4+b^4+c^4

Answer 5

Give me the identities you used sir

Thanks

Answer 6

I go it no need thanks I understand how to manipulate it

Answer 7

I knew it wouldn't take you very long.

Answer 8

Mont — Please do not use tutors' names in the space for your name. Thanks.