the product of two negative numbers is 338. one of the numbers is half the other number. find the numbers.

x y = 338

x = y/2
y^2/2 = 338
y^2 = 676
y = -26
The other number is -13

Yes.

To solve this problem, let's assign variables to the unknown numbers.

Let's say that one of the numbers is 'x', and the other number is 'y'. Since it's given that one number is half the other, we can set up the equation:

x = (1/2)y

Now we know that the product of two negative numbers is 338. We can set up another equation using this information:

xy = 338

Substituting the first equation into the second equation, we get:

(1/2)y * y = 338

Next, we can simplify the equation:

(1/2)y^2 = 338

To solve for 'y', we can multiply both sides of the equation by 2:

y^2 = 676

Taking the square root of both sides, we find:

y = ±√676

y = ±26

Since the numbers are negative, the value of 'y' is -26.

To find 'x', we substitute the value of 'y' into the first equation:

x = (1/2)(-26)
x = -13

So the two numbers are -13 and -26.