If a + b + c = 6, a² + b² + c² = 14 and a³ + b³ + c³ = 36, then the value of abc is

3

6

9

9

(a + b + c)²
$left parenthesis straight a plus straight b plus straight c right parenthesis squared equals space space straight a squared space plus space straight b squared space plus space straight c squared space space plus space 2 left parenthesis ab space plus space bc space plus space ca right parenthesis rightwards double arrow space space 36 space equals space space 14 space plus space 2 left parenthesis ab space plus space bc space plus space ca right parenthesis rightwards double arrow space space space space ab space plus space bc space plus space ca space equals space left parenthesis 36 minus 14 right parenthesis space divided by space 2 rightwards double arrow space space space space ab space space plus space bc space plus space ca space equals space 11$

$therefore space space straight a cubed space plus space straight b cubed space plus space straight c cubed space minus space 3 abc space equals space left parenthesis straight a plus straight b plus straight c right parenthesis thin space left parenthesis straight a squared plus straight b squared plus straight c squared minus ab minus bc minus ca right parenthesis rightwards double arrow space space space space space space space space 36 space minus space 3 abc space equals space 6 left parenthesis 14 minus 11 right parenthesis rightwards double arrow space space space space space space space 36 space minus space 3 abc space equals space 84 space minus space 66 space equals space 18 rightwards double arrow space space space space space space 3 abc space equals space 36 minus 18 space equals space 18 rightwards double arrow space space space space space space abc space equals space space 6$

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If a + b + c = 6, a2 + b2 + c2 = 14 and a3 + b3 + c3 = 36, then the value of abc is 3 6 9 9

Algebra

QA01

If a + b + c = 6, a² + b² + c² = 14 and a³ + b³ + c³ = 36, then the value of abc is

3

6

9

9