SOLUTION: two numbers add up 20 when plusd and 96 when multiplied find the two numbers

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Question 247795: two numbers add up 20 when plusd and 96 when multiplied find the two numbers
Found 2 solutions by solver91311, stanbon:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!






Since , you can say:



Giving you an expression for that can be substituted anywhere you see an . Here's a convenient place:





Simplify into standard form (details left as an exercise for the student):



Now all you have to do is solve the factorable quadratic. You will get two positive roots. can be either number and will be the other.


John

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
two numbers add up 20 when plused and 96 when multiplied find the two numbers
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x + y = 20
xy = 96
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x = 20-y
Substitute into xy=96 to solve for "y":
(20-y)y = 96
-y^2 + 20y = 96
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Rearrange:
y^2 - 20y + 96 = 0
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y = [20 +- sqrt(400 - 4*!*96)]/2
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y = [20 +- sqrt(16)}/2
y = [20 +- 4]/2
y = (20+4]/2 = 12 or y = (20-4)/2 = 8
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Find the true solution(s):
If y = 12, x = 8 and the product is 96
If y = 8, x = 12 and the product is 96
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Cheers,
Stan H.