Question

xy(x-y)=45045. Are there any possible values where, {x,y}€N.
Please reply ASAP.​

Answer 1

Here we notice that the RHS of the equation 45045 is nothing but an odd number. So the LHS of the equation must also be odd, but the following table doesn't let the LHS to be odd.

$\begin {tabular}{|c|c|c|c|c|}\cline{1-5} x & y & xy & x-y & xy(x-y) \\\cline{1-5} odd & odd & odd & even &\bf{even}\\\cline{1-5} odd & even & even & odd &\bf{even}\\\cline{1-5} even & odd & even & odd &\bf{even}\\\cline{1-5} even & even & even & even &\bf{even}\\\cline{1-5}\end {tabular}$

Thus there's no possible solutions for $x,\ y\in\mathbb{N}$ such that $xy(x-y)=45045.$