Question

if+a+++b+++C+is+equal+to+zero+prove+that+a+cube+plus+b+cube+++C+cube+is+equal+to+3+ABC

Answer 1

Step-by-step explanation:

Given: a + b + c =0

Using formula,

${a}^{3} + {b}^{3} + {c}^{3} - 3abc$

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

$= 0 \times ( {a}^{2} + {b}^{2} + {c}^{2} + ab + bc + ca)$

Therefore

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

${a}^{3} + {b}^{3} + {c}^{3} = 3abc$

Hence proved