Question

If a + b + c = 0 and abc = 1, then find the value of a3 + b3 + c3​

Answer 1

3abc

Explanation:

${a}^{3} + {b}^{3} + {c}^{3} - 3abc = (a + b + c)(a ^{2} + {b}^{2} + {c}^{2} - bc - ca - ab)$

Given,

a+b+c=0

$\therefore {a}^{3} + {b}^{3} + {c}^{3} - 3abc = 0$

$\therefore \: {a}^{3} + {b}^{3} + {c}^{3} = 3abc$

Hope it helps you

Answer 2

If a + b + c = 0 and abc = 1, then find the value of a3 + b3 + c3

→Since, a^3+b^3+c^3−3abc=(a+b+c)(a^2+b^2+c^2−bc−ca−ab)

2−bc−ca−ab)Given, a+b+c=0

2−bc−ca−ab)Given, a+b+c=0∴a^3+b^3+c^3−3abc=0

3−3abc=0∴a^3+b^3+c^3=3abc

∴a^3+b^3+c^3=3..........(abc=1)

hope it helps❤