Question

Find the value of a cube + b cube + c cube minus 3abc when a +b+ c =15 and a square + b square +c square =33

Answer 1

Answer:

- 945.

This question uses an identity

Step-by-step explanation:

This is the golden identity :

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

Find the value of

$ab + bc + ca$

from the identity :

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

Thus we can find the answer from the first identity.