2 methods, either know the exact formula (which u should know if/when u do 4u)
a^3+b^3+c^3=(a+b+c)(a^2+b^2+c^2-(ab+bc+ac))+3abc
Here since (a+b+c)=0, then we only focus on 3(abc) which is equal to 3(3/2) = 9/2 (This way is faster, however is prone to mistakes since if you memorise it wrong, then you will get 1/3 max, sometimes even 0/3)
Alternatively you can do it this way (this method is what teachers usually want you to do): Since a,b,c are roots, we can rewrite the cubic equation in the following ways.
2a^3+4a-3=0
2b^3+4b-3=0
2c^2+4c-3=0
Adding up these three equations gives
2(a^3+b^3+c^3)+4(a+b+c)-9=0
Rearranging for a^3+b^3+c^3 gives
[9-4(a+b+c)]/2, which is just (9-0)/2 = 9/2, since (a+b+c)=0
I hope that clears it up for u, there are sometimes questions asking for like a^4+b^4+c^4 and to the power of 5, etc, which u cannot use the first method for since the formula is insanely long
See if you can apply the 2nd method into this question
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