Question

if the centroid of the triangle formed with (a, b), (b, c) and (c, a) is O(0, 0) then a^3+b^3+c^3=​

Answer 1

Answer:

here you go

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Answer 2

Answer:

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

Step-by-step explanation:

$( \frac{a + b + c}{3} \: \: \: \: \: \: \frac{a + b + c}{3} ) = (0 \: \: \: \: \: 0) \\ \\ therefore \: \: \: \: a + b + c = 0 \: \: \: \: \: \: \: \: \: ....(i) \\ \\ then \: \: \: \: {a}^{3} + {b}^{3} + {c}^{3} -3abc = (a + b + c)( {a}^{2} + {b}^{2} + {c}^{2} - ab - bc - ca) \\ \\ = 0( {a}^{2} + {b}^{2} + {c}^{2} - ab - bc - ca) \\ \\ therefore\:\: {a}^{3} + {b}^{3} + {c}^{3}= 3abc.$