Question

a+b+c=15,a^2+b^2+c^2=83 and a^3+b^3+c^3=495 then find the value of abc.Also ab+bc+ca=?....plzz ans my question plzz.... plzzzzzzz

Answer 1

a+b+c=15
a^2+b^2+c^2=83

(a+b+c)²= a²+b²+c² + 2(ab+bc+ca)
15² = 83 + 2(ab+bc+ca)
225 - 83 = 2(ab+bc+ca)
142 = 2(ab+bc+ca)
ab+bc+ca = 142/2
ab+bc+ca = 71

(a+b+c)(a²+b²+c² - (ab+bc+ca))= a³ + b³ + c³ - 3abc
15 (83 - 71) = 495 - 3abc
15(12) = 495 - 3abc
180 = 495 - 3abc
3abc = 495 - 180
3abc = 315
abc = 315/3
abc = 105