?By: Tao Steven Zheng (鄭濤)

【Problem】

Prove why the product of two negative real numbers is a positive real number.

【Solution】

Let ? be two positive real numbers; subsequently, and ?are their respective additive inverses.

A clever way to prove that is to begin by considering the equation

and then use this equation to show that and .

First, factor out from the expression :

Since ,

Thus,

Now, with the original equation, factor out ?from the expression :

Thus,

Since? and , we discover that?

Therefore, the product of two negative numbers is positive.