Let the numbers are x and y
And it is given that the difference is 180
So we have
And let the product is p. So we have
Substituting the value of x , we will get
Differentiating p,
Again differentiating ,
SO we will get minimum.
And to find the minimum, we have to set p' equal to 0 and solve for y.
Back substituting the value of y, we will get
So the numbers are 90 and -90 .