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What two numbers equal -45 while multiplying and -12 while adding?

 Dec 5, 2018
edited by Guest  Dec 5, 2018
 #1
avatar+5226 
+1

\((x+y)=-12\\ xy = -45\\ y=-12-x\\ x y = x(-12-x)=-45\\ x(12+x) = 45\\ x^2 + 12x -45 = 0\\ (x+15)(x-3) = 0\\ x=-15 \text{ or }x=3 \\ y=3 \text{ or }y=-15\\ \text{so we see that the two numbers are }-3 \text{ and }15\)

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 Dec 5, 2018
 #2
avatar+18460 
+1

Another means:

 

x+y = 12    so x = -12-y

x*y=-45     Sub x=12-y in to this

(-12-y)y =-45

-y^2-12y +45 = 0 

y^2+12y-45=0            now use quadratic formula to find x = -15 and 3

 Dec 5, 2018

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