SOLUTION: Find two numbers whose sum is 19 and the product is 48

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Question 985353: Find two numbers whose sum is 19 and the product is 48
Found 2 solutions by Edwin McCravy, Alan3354:
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Find two numbers whose sum is 19 and the product is 48
system%28x%2By=19%2C%0D%0Axy=48%29

y=19-x

xy=48
x(19-x)=48
19x-x² = 48
-x²+19x-48 = 0

a=-1, b=19, c=-48

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+



x+=+%28-19+%2B-+sqrt%28361-192+%29%29%2F%28-2%29+

x+=+%28-19+%2B-+sqrt%28169+%29%29%2F%28-2%29+

x+=+%28-19+%2B-+13%29%2F%28-2%29+

Using the +

x+=+%28-19+%2B+13%29%2F%28-2%29+

x+=+%28-6%29%2F%28-2%29+

x+=+3

x+=+3, 
y=19-x
y=19-3
y=16
      
So 3+16 = 19,  3*16 = 48

Using the -

x+=+%28-19+-+13%29%2F%28-2%29+

x+=+%28-32%29%2F%28-2%29+

x+=+16

x+=+16, 
y=19-16
y=19-16
y=3
      
So 16+3 = 19,  16*3 = 48

Not really a different answer, just swapping the letters.

Answer: 3 and 16

Edwin

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find two numbers whose sum is 19 and the product is 48
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Check for integer solutions first.
Find a pair of factors of 48 with a sum of 19.
----
eg,
1*48 NG
2*24 NG
3*16 That's it.