Question

A+b+c=4
a^2+b^2+c^2=10
a^2+B^3+C^3=22
a^4+b^4+c^4=?

Answer 1

I think it's 46 or 6

Explanation:

`2(ab+bc+ca)=(a+b+c)^2-(a^2+6^2+c^2)`

=>
`2(ab+bc+ca)=1^2-2=-1`

=>
`ab+bc+ca=-1/2`

Given

`a^3+b^3+c^3=3`

=>
`a^3+b^3+c^3-3abc+3abc=3`

=>
`(a+b+c)(a^2+b^2+c^2-ab-bc-ca)+3abc=3`

=>
`(a+b+c)(a^2+b^2+c2-(ab+bc+ca)+3abc=3`

=>
`(1*(2-(-1/2) +3abc))=3`

=>
`(2+1/2)+3abc=3`

=>
`abc=1/6`

Now

`a^4+b^4+c^4`

`=(a^2+b^2+c2^)^2-2)a^2b^2+b^2c^2+c^2a^2)`

`= 2^2-2*(-1/12)`

`=4+1/6=4(1)/(6)`

Yes, there is more things to do but I don't want it more challenging

Therefore

`a^5+b^5+c^5=6-0=6`

Using memory and doing it a easier way, I think it's 46. Using paper and pencil, think it's 6