Question

38. If a + b + c = 5, a2 + b2 + c2 = 29 and abc =-24, find
the value of a3+be+c3​

Answer 1

Answer:

$( {a}^{3} + {b}^{3} + {c}^{3} ) = 71$

Explanation:

$a + b + c = 5 \: \: \: \: \: \: ....(i)$

${a}^{2} + {b}^{2} + {c}^{2} = 29 \: \: \: \: \: .......(ii)$

$abc = - 24 \: \: \: \: \: \: .....(iii)$

we know that

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

using these to find value of ( ab + bc + ca )

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

$25 - 29 = 2(ab + bc + ca)$

$ab + bc + ca = 2 \: \: \: \: \: \: .....(iv)$

we also know one more identity

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

$putting \: all \: value \: from \: (i) \: (ii) \: (iii) \: (iv)$

${5}^{3} = ( {a}^{3} + {b}^{3} + {c}^{3} ) + 3(5)(2) - 3( - 24)$

$125 = ( {a}^{3} + {b}^{3} + {c}^{3} ) + 30 - ( - 24)$

$125 = ( {a}^{3} + {b}^{3} + {c}^{3} ) + 30 + 24$

$( {a}^{3} + {b}^{3} + {c}^{3} ) = 125 - 54$

$( {a}^{3} + {b}^{3} + {c}^{3} ) = 71$

hope it helps u . Mark this answer as brainleists

Answer 2

Explanation:

It's right mate which is written above