Question

Find the value of a cube + b cube + c cube if a+b+c=5 and a square+b square + c square=29
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Answer 1

Answer:

Given

$a + b + c = 5$

${a}^{2} + {b}^{2} + {c}^{2} = 29$

so,

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

${5}^{2} = 29 + 2(ab + bc + ca)$

$ab + bc + ca = \frac{25 - 29}{2} = - 2$

now,

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

${a}^{3} + {b}^{3} + {c}^{3} - 3abc =5 \times (29 - ( - 2)) = 5 \times 31 = 155$