Final answer:
To solve this problem, represent the consecutive even numbers as x, (x + 2), and (x + 4). Then equate the product of the first two numbers to 6 less than 9 times the third number. Solve the resulting quadratic equation to find the values for x. The consecutive even numbers are 10, 12, and 14.
Step-by-step explanation:
To solve this problem, let's represent the consecutive even numbers as x, (x + 2), and (x + 4).
The product of the first two numbers is (x)(x + 2) = x^2 + 2x.
9 times the third number is 9(x + 4) = 9x + 36.
According to the problem, the product of the first two numbers is 6 less than 9 times the third number, so we have the equation x^2 + 2x = 9x + 36 - 6.
Simplifying the equation gives us x^2 - 7x - 30 = 0.
Factoring the quadratic equation gives us (x - 10)(x + 3) = 0.
So the possible values for x are 10 or -3.
Therefore, the consecutive even numbers are 10, 12, and 14.