If xy(x + y) = m, then the value of x3 + y3 + 3m is?
A. $$\frac{{{m^3}}}{{xy}}$$
B. $$\frac{{{m^3}}}{{{{\left( {x + y} \right)}^2}}}$$
C. $$\frac{{{m^3}}}{{{x^3}{y^3}}}$$
D. $$\frac{m}{{{x^3}{y^3}}}$$
Answer: Option C
Solution (By Examveda Team)
$$\eqalign{ & xy\left( {x + y} \right) = m \cr & {\text{find }}{x^3} + {y^3} + 3m \cr & xy\left( {x + y} \right) = m\, . . . . . (i) \cr & \left( {x + y} \right) = \frac{m}{xy} \cr &{\text{Cubing both side}} \cr & \Rightarrow {x^3} + {y^3} + 3.xy\left( {x + y} \right) = \frac{{{m^3}}}{{{x^3}{y^3}}} \cr & {\text{From equation (i)}} \cr & \Rightarrow {x^3} + {y^3} + 3.m = \frac{{{m^3}}}{{{x^3}{y^3}}} \cr & \Rightarrow {x^3} + {y^3} + 3m = \frac{{{m^3}}}{{{x^3}{y^3}}} \cr} $$This Question Belongs to Arithmetic Ability >> Algebra
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