Question

If $x-y=5$ and $xy=84,$ then find the value of $x^3-y^3$

Answer 1

Given : $x-y=5$, and $xy=84$

By using the formula : $(x-y{)}^3=x^3-y^3-3x^{2}y+3x{y}^2$

$x^3-y^3=(x-y{)}^3+3x^{2}y-3x{y}^2$

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

By substituting the given values, we get :

$=[5{]}^3+3\times 84\times [5]$

$=125+1260$

$=1385$

$\therefore x^3-y^3=1385$