anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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Savvy
  • Savvy
they can have 60 and 52 as products but not 80....
anonymous
  • anonymous
how did you find that?
anonymous
  • anonymous
the highest possible product you can get is (17/2)^2

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anonymous
  • anonymous
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
anonymous
  • anonymous
what is x?
anonymous
  • anonymous
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)
anonymous
  • anonymous
for b) it's 4 and 13, you can use the same strategy
anonymous
  • anonymous
thank u soo much :D
anonymous
  • anonymous
Nicely done
Savvy
  • Savvy
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.
anonymous
  • anonymous
@ m_charron2 I don't get the part for the second number a)
anonymous
  • anonymous
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
anonymous
  • anonymous
ok thnxx

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