Question

Two numbers that differ by 46

Answer 1

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

$x-y=46\\ y=x-46$-----> equation 1

$P=x*y$-----> equation 2

substitute equation 1 in equation 2

$P=x*[x-46]\\ P=x^{2} -46x$

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 $(23,-529)$

that means, for $x=23$

the product is a minimum $P=-529$

find the value of y

$y=x-46\\ y=23-46\\ y=-23$

therefore

the answer is

the numbers are $23$ and $-23$

Answer 2

Choose any two numbers that when you subtract one from the other, you get 46

For example:
56 and 102, between them there's a difference of 46 units

Another example:
89 and 135