Solving eqns: Find 2 pos. numbers whose difference is 9 and

What have you tried? How far have you gotten?

Please be specific, starting with the variables you picked and what they stand for.

Thank you.

Eliz.
 
solving equations

Let x be one number and y be the other number. The first equation is x-y=9, the second I think is xy is a minimum.

x-y=9 xy
x=y+9 (y+9)y
y^2 +9y
y^2+9y+20.25-20.25
x-(-4.5)=9 (y+4.5)^2-20.25
x+4.5=9 y+4.5=0
x=4.5 y=-4.5
But these aren't positive numbers.
 
You might want to consider this approach.

Let x = the smaller number
Then x + 9 = the larger number

Let y = the product of the two numbers.

y = x(x + 9)
y = x^2 + 9x

This is a parabola which opens upward. The minimum value of y occurs at the vertex of the parabola....

Does that give you something to work with?
 
irene girvin said:
The answer doesn't give two positive numbers.
Click to expand...
What answer did you get when you completed the solution from "y = x<sup>2</sup> + 9x"?

Please be specific, showing all of your work and reasoning. Thank you.

Eliz.
 
Find 2 positive numbers whose difference is 9 and whose product is a minimum.

Unless I am missing some subtle clue, if both numbers must be positive, why not 10 and 1????

10 - 1 = 9 and 10(1) = 10
 
TchrWill said:
Find 2 positive numbers whose difference is 9 and whose product is a minimum.

Unless I am missing some subtle clue, if both numbers must be positive, why not 10 and 1????

10 - 1 = 9 and 10(1) = 10
Click to expand...

Well, 1 *10 = 10

But, what if x = .5? Then x + 9 = 9.5....and .5*9,5 = 4.75....that's certainly less than 10!

I am "stuck" on this problem....I think that as x approaches 0 from the right, the product gets smaller and smaller. But, I don't know at which value of x you'd get a minimum product with both x and x + 9 being positive...in fact, I'm not sure you CAN find one.
 
Agree, Mrspi.

9 1/1000000 - 1/1000000 = 9

9 1/1000000 * 1/1000000 = .000000000001
 
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