How to solve these three equations? If α ,β ,γ are three numbers s.t.:
$\ α^ \ $ + $\ β \ $ +  $  γ \ $ = −2
$\ α^2 \ $ + $\ β^2 \ $ +  $  γ^2 \ $ = 6
$\ α^3 \ $ + $\ β^3 \ $ +  $  γ^3 \ $ = −5,
then $\ α^4 \ $ + $\ β^4 \ $ +  $  γ^4 \ $ is equal to ??
I tried out substituting the values of each equation to one other ...but it became very 
complex .. I also remember some crammers rule for this ..using matrices??
Is that the way??  

Let $A_{n}=a^n+b^n+c^n$. Then we have
$$A_{n+3}=(a+b+c)A_{n+2}-(ab+bc+ac)A_{n+1}+abcA_{n}$$
and
$$2(ab+bc+ac)=(a+b+c)^2-(a^2+b^2+c^2)=4-6=-2$$
$$a^3+b^3+c^3=(a+b+c)^3-3(a+b+c)(ab+bc+ac)+3abc$$
Then we can easily find $abc$.
