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
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