quadratic

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quadratic

Find two positive numbers whose difference is 27 and whose product is 2680.
Proof Proof
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Re: quadratic

x = one positive number
y = other positive number

x - y = 27   ← difference is 27
xy = 2680   ← product is 2680

x - y = 27   ← first equation
x = y + 27   ← added y to each side

xy = 2680   ← second equation
(y + 27)y = 2680   ← substituted (y + 27) for x
y² + 27y = 2680   ← distributive property
y² + 27y - 2680 = 0   ← subtracted 2680
(y + 67)(y - 40) = 0   ← factored
y + 67 = 0   or   y - 40 = 0   ← set equal to zero
y = -67   or   y = 40   ← solved

40 and 67 are the two numbers

- Proof