A,b,c are three numbers solve the following

a+b+c=-2
a^2+b^2+c^2=6
a^3+b^3+c^3=-5
then what is a^4+b^4+c^4=?????

how to solve such types of questions?

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a + b + c = -2 ............ [1]
a^2 + b^2 + c^2 = 6 ................. [2]
a^3 + b^3 + c^3 = -5 ................. [3]

[1]^2:
(a + b + c)^2 = (-2)^2
a^2 + b^2 + c^2 + 2ab + 2ac + 2bc = 4
6 + 2(ab + ac + bc) = 4
ab + ac + bc = -1 ............. [4]

[1]^3:
(a + b + c)^3 = (-2)^3
a^3 + b^3 + c^3 + 3ab(a + b) + 3ac(a + c) + 3bc(b + c) + 6abc = -8
-5 + 3ab(-2 - c) + 3ac(-2 - b) + 3bc(-2 - a) + 6abc = -8
-5 - 6(ab + ac + bc) - 3abc = -8
-5 - 6(-1) - 3abc = -8
abc = 3 ................. [5]

[2]^2:
a^4 + b^4 + c^4 + 2(a^2 b^2 + a^2 c^2 + b^2 c^2) = 6^2
a^4 + b^4 + c^4 + 2[ (ab + ac + bc)^2 - 2a^2 bc - 2ab^2 c - 2abc^2 ]
a^4 + b^4 + c^4 + 2[ (ab + ac + bc)^2 - 2abc(a +b + c) ] = 36
a^4 + b^4 + c^4 + 2[ (-1)^2 - 2(3)(-2) ] = 36
a^4 + b^4 + c^4 = 10

Confirmation:
http://www.wolframalpha.com/input/?i=a%2…

No, I don't think there is one.

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