Question

calc

Answer 1

guess, i bet you are right

Answer 2

i bet not- i got 33

Answer 3

33 and what is the other?

Answer 4

You need to represent these 2 unknowns with letters, e. g., x and y.

Now, how would you write "product of these 2 unknowns" in terms of x and y?
How would you write "sum of these 2 unknowns" in terms of x and y?

Answer 5

If you do this correctly, you'll have 2 simult. equations in x and y and should be able to solve for both. You are only expected to cough up ONE of these 2 numbers as your answer. I think that's silly. I'd calculate nd present both as my answer.

Answer 6

Note that others could help you more (with more specific info) if you'd share any work you've done.

Answer 7

@3mar please:-)

Answer 8

I am doing it myself!

Answer 9

actually, i lied, guessing is not a good idea here
do what @mathmale said, takes not too long

Answer 10

@3mar ok:-)

Answer 11

So:
Let x & y= some positive integer

Than: xy=196
& y= 196/x

Than: x+y=f(x)

x+196^(-x)=f(x)
Take the derivative --> Find all critical points --> Minimize for x

Next: Solve for y ^^

Answer 12

@iwanttogotostanford ?

Answer 13

I'm sorry...

\[f(x)=x+196x^{-1}\]

Answer 14

but @sunnnystrong, if we were doing to find the first derivative of this function, we would have imaginary conjugates, and have not real roots!

How did you do it?

Answer 15

So:

If
\[f(x)=x+196x^{-1}\]

Than f'(x)--->

\[f'(x)=1-196x^{-2}\]

Solving for critical points:

\[0=1-196x^{-2}\]
\[0=1-\frac{ 196 }{ x^2 }\]

*Multiply everything by x^2 to clear fractions

\[0=x^2-196]

x=14

Answer 16

Let the 2 positive integers be x and y.
Then their product is written as xy=196.
Their sum is x+y, which sunnystrong has named "f(x)."

You can choose to eliminate either x or y. Sunnystrong has chosen to elim. y by solving xy=196 for y: y=196/x. That's correct.

Now, maximize the function xy, which in terms of x alone is x + 196/x.

Yes, this can be rewritten as f(x) = x + 196/x

Answer 17

sunnystrong is right on target!

What's the other positive integer?

Answer 18

@mathmale
Thanks!

Answer 19

@sunnystrong: My pleasure.

Answer 20

Sunnystrong was minimizing the SUM of x and y, otherwise known as f(x) = x + 196/x

Answer 21

@sunnnystrong

I think you should have \(\pm14\), not just 14, as it is the square root of 196!!!

Answer 22

@3mar: The directions call for two POSITIVE integers. Can you figure out what another positive integer would be?

Answer 23

Oh sorry...
I got it!

TWO POSITIVE integers, so we would exclude the negtive ones!

Sorry I got it!


Thank you for good explanation, @sunnnystrong.
Thank you very much.

Answer 24

@3mar .. but 196 is a perfect square root :P so no +/-

Answer 25

\[\sqrt{196}=\pm 14\]
Put I got it, "we would exclude the negtive ones!"

Answer 26

Is it possible that the TWO POSITIVE INTEGERS are 14 and 14, both positive?

Is the product of 14 and 14 equal to 196?

Answer 27

Time for pray - 45 min - Salam!