Question

O2 If a+b+c= 6 and ab + bc +ca =11 and abc =-1find a3 +b3 +c3​

Answer 1

$( {a + b + c})^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2(ab + bc + ca) \\ {6}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2 \times 11 \\ 36 - 22 = {a}^{2} + {b}^{2} + {c}^{2} \\ {a}^{2} + {b}^{2} + {c}^{2} = 14 \\ now \: \: \: {a}^{3} + {b}^{3} + {c}^{3} = (a + b + c)( {a}^{2} + {b}^{2} + {c}^{2} - ab - bc - ca) + 3abc \\ = 6(14 - 11) + 3( - 1) \\ = 18 - 3 \\ {a}^{3} + {b}^{3} + {c}^{3} = 15$