yolo tengo
Well-Known Member
- Joined
- Sep 2, 2022
- Messages
- 807
- Gender
- Undisclosed
- HSC
- 2024
Students helping students, join us in improving Bored of Studies by donating and supporting future students!
hii thank you sm!! what's the name of the 2nd method if you don't mind me asking?? and yes, i'll give the question a go for sure.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 questionView attachment 39348
theres isnt really a name for it, just a method to solve these type of questionshii thank you sm!! what's the name of the 2nd method if you don't mind me asking?? and yes, i'll give the question a go for sure.![]()
ohhh haha, thank youtheres isnt really a name for it, just a method to solve these type of questions![]()
yo i am practically brain dead atm i feel like i know how to get to the end but its not clicking in my head or maybe i'm doing this wrongSee if you can apply the 2nd method into this questionView attachment 39348
sshhhthats not my working![]()