Question

If $x+y=12$ and $xy=27$, find the value of $x^3+y^3$.

Answer 1

Given that, $x+y=12$ and $xy=27$

We know,

$(x+y{)}^3=x^3+y^3+3xy(x+y)$

Therefore,

${12}^3=x^3+y^3+3\times 27\times 12$

$1728=x^3+y^3+972$

$x^3+y^3=1728-972=756$

$\therefore x^3+y^3=756$