Question

4. Find the value of m3 + n3 - 9mn, if m + n + 3 = 0.​

Answer 1

Step-by-step explanation:

Important Property:

$if \: a + b + c = 0$

$then \: {a}^{3} + {b}^{3} + {c}^{3} = 3abc$

Note:

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

Solution:

Here,

$m + n + 3 = 0$

$= > {m}^{3} + {n}^{3} + {3}^{3} = 3 \times m \times n \times 3$

$= > {m}^{3} + {n}^{3} + 27 = 9mn$

$= > {m}^{3} + {n}^{3} - 9mn = - 27$

Hope this helps!