Question

Find two numbers whose difference is 120 and whose product is a minimum.

Answer 1

200 - 120 = 80 the difference means to subtract

Answer 2

Let the numbers be x & y

Let x > y

So as the difference of the numbers is 120

We get x - y = 120

Subtracting 120 from both sides and adding y we get

y= x – 120

Now the product of the numbers be P

P= xy

P = x(x-120)

P = x² - 120x

Comparing with
`ax^2+bx+c`

We get

a= 1 & b = -120

The vertex is (h,k)

Where

h = -b/2a = -(-120)/2 = 60

So one part of the number shall be x= 60

Now y = x - 120 = 60 - 120 = -60

The numbers are -60 & 60.