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5 votes
The difference of two numbers is 70. Find the two numbers so their product is as small as

possible.

User Jake Long
by
6.3k points

1 Answer

4 votes

Answer:

-35, 35

Explanation:

let one of the numbers be x.

It is given that the difference between the 2 numbers is 70. In order for this statement to be true, the other number must be (x + 70)

so now we have our 2 numbers x and (x + 70)

let y = the product of our 2 numbers

hence,

y = x (x + 70) , or

y = x² + 70x

We recognize this to be a quadratic equation and we can immediately concluded some things:

1) the x² term is positive, hence it must be a quadratic graph with a minimum vertex (i.e the graph looks like a u-shape and not an n-shape)

2) the minimum point is located at x = -b/2a.

in our case, b = 70 and a = 1,

hence the for y to be minimum,

x = -(70) / 2(1) = -70/2

x = -35 (answer)

therefore the 2nd number

= x + 70

= -35 + 70

= 35 (answer)

User CargoMeister
by
5.9k points
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