The difference between two numbers is 3. If the square of the smaller number is equal to 4 times the larger number, find the numbers.

**x = larger number**

y = smaller number

y = smaller number

x - y = 3 {difference between two numbers is 3}

y² = 4x {square of smaller is equal to 4 times the larger}

y = x - 3 {added y and subtracted 3 from each side in top original equation}

(x - 3)² = 4x {substituted (x - 3), in for y, into bottom original equation}

x² - 6x + 9 = 4x {squared the binomial by multiplying by itself}

x² - 10x + 9 = 0 {subtracted 4x from each side}

(x - 9)(x - 1) = 0 {factored into two binomials}

x - 9 = 0 or x - 1 = 0 {set each factor equal to 0}

x = 9 or x = 1 {solved each equation for x}

y = x - 3

y = 9 - 3 or y = 1 - 3 {substituted 9 and 1 for x into y = x - 3}

y = 6 or y = -2

**9 and 6**

or

**1 and -2**are the sets of numbers

**- Algebra House**