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
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
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
