MATH SOLVE

2 months ago

Q:
# One number is 4 less than twice a second number. find a pair of such numbers so that their product is as small as possible.

Accepted Solution

A:

For this case, the first thing we must do is define a variable.

We have then:

x: unknown number.

First number: 2x - 4

Second number: x

The product of the numbers is:

[tex] y = x (2x-4) [/tex]

Rewriting:

[tex] y = 2x ^ 2-4x [/tex]

Deriving the equation we have:

[tex] y '= 4x-4 [/tex]

We equal zero and clear x:

[tex] 4x - 4 = 0 x = 4/4 x = 1[/tex]

Then, the first number is:

[tex] 2x - 4 = 2 (1) - 4 = 2 - 4 = - 2 [/tex]

Answer:

First number: -2

Second number: 1

We have then:

x: unknown number.

First number: 2x - 4

Second number: x

The product of the numbers is:

[tex] y = x (2x-4) [/tex]

Rewriting:

[tex] y = 2x ^ 2-4x [/tex]

Deriving the equation we have:

[tex] y '= 4x-4 [/tex]

We equal zero and clear x:

[tex] 4x - 4 = 0 x = 4/4 x = 1[/tex]

Then, the first number is:

[tex] 2x - 4 = 2 (1) - 4 = 2 - 4 = - 2 [/tex]

Answer:

First number: -2

Second number: 1