The product of two numbers is 323 and the difference between them is 2. What are the two numbers?

**x = one number**

**y = other number**

xy = 323 {product of two numbers is 323}

x - y = 2 {difference between the two numbers is 2}

x = y + 2 {re-arranged second equation}

(y + 2)(y) = 323 {substituted (y + 2), in for x, into top equation}

y² + 2y = 323 {used distributive property}

y² + 2y - 323 = 0 {subtracted 323 from each side}

(y + 19)(y - 17) = 0 {factored into two binomials}

y + 19 = 0 or y - 17 = 0 {set each factor equal to 0}

y = -19 or y = 17 {solved each equation for y}

x = y + 2 {bottom re-arranged equation}

x = -19 + 2 or x = 17 + 2 {substituted -19 and 17, in for y, into bottom re-arranged equation}

x = -17 or x = 19 {solved each equation for x}

**-17 and -19**

or

19 and 17

or

19 and 17

could be the two numbers

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