### Instruction: What is the greatest product obtainable from two integers whose sum is 246?### Response: So we have two numbers, x and y, which add up to 246.
Right. So we can say x + y = 246.
We want to find the greatest product, which we can call z. So z = x * y.
Yes. But since we know x + y = 246, we can solve for y and substitute it in the equation for z.
That's right. So y = 246 - x. Then z = x * (246 - x).
Now we can distribute x. So z = 246x - x^2.
Right. Now we can take the derivative of z. So dz/dx = 246 - 2x.
And we can set that equal to 0 to find the maximum value. So 246 - 2x = 0.
That means x = 123. And since x + y = 246, y = 123 as well.
So the two numbers are 123 and 123.