Question

if a + b + C is equal to 15 at a square + b square + c square equal to 83 then find the value of a cube plus b cube plus c cube minus 3 ABC

Answer 1

$a + b+ c = 15 \\ {a}^{2} + {b}^{2} + {c}^{2} = 83\\ ( a+ b +c ) {}^{2} = (15) {}^{2} \\ {a}^{2} + {b}^{2} + {c}^{2} + 2( ab+ bc+ ca) = 225 \\ 83 + 2(ab + bc+ ca) = 225 \\ 2( ab+ bc+ ca) = 225 - 83 \\ ab + bc + ca = \frac{142}{2} \\ ab+bc + ca = 71$
${a}^{3} + {b}^{3} + {c}^{3} - 3abc \\ = (a + b + c)( {a}^{2} + {b}^{2} + {c}^{2} - (ab + bc + ca) \: ) \\ = (15)(83 - 71) \\ = 15 \times 12 \\ = 180$
$so \\ a {}^{3} + {b}^{3} + {c}^{3} - 3abc = 180$



--------Hope this will help you---------

Answer 2

Hey friend

Here is your ans

in the given photo attachment__________________




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