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 ++++++++
Follow Math Help Forum on Facebook and Google+
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
Last edited by Moo; Aug 23rd 2008 at 03:21 AM. Reason: major mistake
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
View Tag Cloud