Ipick two whole numbers $x$ and $y$ between $1$ and $10$ inclusive (not necessarily distinct). my friend picks two numbers $x -4$ and $2y-1$. if the product of my friend's numbers is one greater than the product of my numbers, then what is the product of my numbers?

Step-by-step explanation:

We have a quadratic equation in z, given as:

with roots

The sum of roots is given by:

This implies that

Also product of roots is given by:

This implies that:

Therefore

really really sorry if i'm

-12 -5(x + 4) = 3x

-12 - 5x - 20 = 3x

-12 - 20 - 5x = 3x

-32 - 5x = 3x

    + 5x   + 5x

-32 = 8x

8         8

- 4= x