the complete question is
Find two numbers whose difference is 46 and whose product is a minimum
Let
x------->larger number
y-------> smaller number
P-------> product of the two numbers
we know that
-----> equation 1
-----> equation 2
substitute equation 1 in equation 2
![P=x*[x-46]\\ P=x^(2) -46x](https://img.qammunity.org/2018/formulas/mathematics/high-school/bwhxdrnjn59aqb2kung6t9o74dy4bf6yuv.png)
using a graph tool
see the attached figure
Find the value of x for that the product P is a minimum
the vertex is the point

that means, for

the product is a minimum

find the value of y

therefore
the answer is
the numbers are
and
