Two numbers that differ by 46

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

Answer Link

calculista calculista · Answer 2 · 2018-07-19T01:18:50+02:00

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

[tex] x-y=46\\ y=x-46 [/tex]-----> equation 1

[tex] P=x*y [/tex]-----> equation 2

substitute equation 1 in equation 2

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

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 [tex] (23,-529) [/tex]

that means, for [tex] x=23 [/tex]

the product is a minimum [tex] P=-529 [/tex]

find the value of y

[tex] y=x-46\\ y=23-46\\ y=-23 [/tex]

therefore

the answer is

the numbers are [tex] 23 [/tex] and [tex] -23 [/tex]