Deterime whether two real numbers whose sum is 17 can have each of the following products. If so, find the real numbers.
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they can have 60 and 52 as products but not 80....
how did you find that?
the highest possible product you can get is (17/2)^2
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a) x(17-x) = 60
-(x-8,5)^2 + 72.25=60
(x-8,5)^2 = 12.25
x-8,5 = sqrt(12.25)
x = 5
what is x?
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)
for b) it's 4 and 13, you can use the same strategy
thank u soo much :D
let the numbers be x and y....
now, x+y = 17
xy=P P:product of x and y
17x - x^2 = P
x^2 - 17x + P = 0
it's discriminent, D = 289 - 4P
only for P=60 and P=52
which means only for these values there is a real value of x.
@ m_charron2 I don't get the part for the second number a)
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