If xy(x + y) = m, then the value of x³ + y³ + 3m is?

1 $\frac{m^{3}}{x y}$ $\frac{{{m^3}}}{{xy}}$
2 $\frac{m^{3}}{{(x + y)}^{2}}$ $\frac{{{m^3}}}{{{{\left( {x + y} \right)}^2}}}$
3 $\frac{m^{3}}{x^{3} y^{3}}$ $\frac{{{m^3}}}{{{x^3}{y^3}}}$
4 $\frac{m}{x^{3} y^{3}}$ $\frac{m}{{{x^3}{y^3}}}$

Answer:- 1

Explanation:-

Solution:

\begin{aligned} x y (x + y) = m \\ find x^{3} + y^{3} + 3 m \\ x y (x + y) = m . . . . . (i) \\ C u b i n g b o t h s i d e \\ \Rightarrow x^{3} + y^{3} + 3. x y (x + y) = \frac{m^{3}}{x^{3} y^{3}} \\ From equation (i) \\ \Rightarrow x^{3} + y^{3} + 3. m = \frac{m^{3}}{x^{3} y^{3}} \\ \Rightarrow x^{3} + y^{3} + 3 m = \frac{m^{3}}{x^{3} y^{3}} \end{aligned}

$\eqalign{ & xy\left( {x + y} \right) = m \cr & {\text{find }}{x^3} + {y^3} + 3m \cr & xy\left( {x + y} \right) = m\,.....(i) \cr & Cubing{\text{ }}both{\text{ }}side \cr & \Rightarrow {x^3} + {y^3} + 3.xy\left( {x + y} \right) = \frac{{{m^3}}}{{{x^3}{y^3}}} \cr & {\text{From equation (i)}} \cr & \Rightarrow {x^3} + {y^3} + 3.m = \frac{{{m^3}}}{{{x^3}{y^3}}} \cr & \Rightarrow {x^3} + {y^3} + 3m = \frac{{{m^3}}}{{{x^3}{y^3}}} \cr}$