Question

Deterime whether two real numbers whose sum is 17 can have each of the following products. If so, find the real numbers.

a) 60
b) 52
c) 80

Answer 1

they can have 60 and 52 as products but not 80....

Answer 2

how did you find that?

Answer 3

the highest possible product you can get is (17/2)^2

Answer 4

a) x(17-x) = 60
-x^2+17x=60
-(x-8,5)^2 + 72.25=60
(x-8,5)^2 = 12.25
x-8,5 = sqrt(12.25)
x = 5

Answer 5

what is x?

Answer 6

x is one of the 2 numbers. the product I wrote on the first line was x (on of the numbers) times 17 -x (since the sum of both numbers is 17, 17 minus one of the numbers will give you the other one)

Answer 7

for b) it's 4 and 13, you can use the same strategy

Answer 8

thank u soo much :D

Answer 9

Nicely done

Answer 10

let the numbers be x and y....
now, x+y = 17
xy=P P:product of x and y
now y=17-x
so x(17-x)=P
17x - x^2 = P
x^2 - 17x + P = 0
it's discriminent, D = 289 - 4P
only for P=60 and P=52
D>0
which means only for these values there is a real value of x.

Answer 11

@ m_charron2 I don't get the part for the second number a)

Answer 12

I skipped the y step. So you're looking for 2 numbers, let's take one number as x, the other as y
As Savvy did, x+y =17 and x*y = 60
so, you isolate one (I chose to isolate y) : y =17 - x
Then substitue y in the second equation : x*(17-x) = 60
Once you get x, simply replace it in either equation to get y

Answer 13

ok thnxx