Question

29. If atbtc-9 and a2 +62+c²=29, then value
of a3 + b3 + c3-3abc​

Answer 1

Answer:

$a + b + c = 9$

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

so,

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

${9}^{2} = 29 + 2(ab + bc + ca)$

$2(ab + bc + ca) = 81 - 29 = 52$

$ab + bc + ca = \frac{52}{2} = 26$

now,

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

${a}^{3} + {b}^{3} + {c}^{3} - 3abc =9 \times (29 - 26) = 9 \times 3 = 27 \: \: ans$