Thread: cubic formula

Q). Let a,b,c be the roots of x^3 + 2x^2 + 7x + 1 = 0.
Obtain A^3 +b^3 +C^3

SOLUTION).
a + b + c = -2
ab + bc + ca = 7
abc = -1
Now what is (a + b+ c)^3 = a^3 + b^3 + c^3 ++++++++

Hello,

Originally Posted by puneet

Q). Let a,b,c be the roots of x^3 + 2x^2 + 7x + 1 = 0.
Obtain A^3 +b^3 +C^3

SOLUTION).
a + b + c = -2
ab + bc + ca = 7
abc = -1
Now what is (a + b+ c)^3 = a^3 + b^3 + c^3 ++++++++

I'll do it quite a rough way, I haven't thought of something simpler yet.





We'll take care of the red part.

Factor as much as possible :


Substitute from :



Thus




Thus

a^3 +b^3 +c^3=(a+b+c)^3+3abc-3(a+b+c)(ab+bc+ca)
=(-2)^3 +3(-1) -3(-2)(7)
=-8-3+42
=31 ans
Is this right

Originally Posted by puneet

a^3 +b^3 +c^3=(a+b+c)^3+3abc-3(a+b+c)(ab+bc+ca)
=(-2)^3 +3(-1) -3(-2)(7)
=-8-3+42
=31 ans
Is this right

Yup
Pardon me, I didn't know this factorisation and I made a mistake