Question

3.1 Q17

Answer 1

Here, you are looking at two numbers, x and y, such that $|x-y|=18$, or, if you say that x is the larger of the two, simply $x-y=18$. You are looking to minimize the value for $xy$. The smallest possible numbers are $x=9, y = -9$. You might initially be tempted to think that you should choose an infinitely negative number and a number 18 more than it; however, the product of two negative numbers is positive, so this would become an infinitely large number. Then, it might be tempting to say 18 and 0, because their product, after all, is zero. But it is possible to get a negative product with a positive and a negative number. The least product is when $y = -x$, and this will apply for any difference you choose, not just 18.

In sum, it's 9 and –9.