Question

If a,b are the roots of ax^2+bx+c=0, find the value of (a^3+b^3)-3ab(a^2+b^2)
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ANSWER = (3abc+6ac^2-b^3-3b^2c)/a^3

Answer 1

you have a + b = -b/a and ab = c/a

and a^3 + b^3 = (a+b)^3 - 3ab(a+b)
a^2 + b^2 = (a+b)^2 - 2ab
can you proceed now?

Answer 2

yup

Answer 3

(a+b)^3 - 3ab(a+b) - 3ab ((a+b)^2 - 2ab)

Answer 4

this will be the whole expansion right?

Answer 5

yes!!

Answer 6

I am stuck here

Answer 7

\[-\frac{ b^3 }{ a^3 }+\frac{ 3bc }{ a^2 }-\frac{ 3c }{ a }(\frac{ b^2-2ac }{ a^2 })\]

Answer 8

ok I've done it