The product of two consecutive positive even numbers is 840. What are the numbers? (Enter solutions from smallest to largest.)
x(x+2) = 840
x^2 + 2x - 840 = 0
(x+30)(x-28) = 0
28 , 30
Assume f(x) = x2 + 2. Find the functional value requested.
CR 7
To find the consecutive even numbers, we need to set up an equation based on the given information.
Let's assume the first even number as 'x', then the next consecutive even number will be 'x + 2'.
According to the problem, the product of these two numbers is 840. We can set up the equation as follows:
x * (x + 2) = 840
Expanding the equation:
x^2 + 2x = 840
Rearranging the terms:
x^2 + 2x - 840 = 0
Now, we can solve this quadratic equation to find the values of 'x' by factoring or using the quadratic formula.
Factoring:
(x - 20)(x + 42) = 0
Setting each factor equal to zero:
x - 20 = 0 or x + 42 = 0
Solving for 'x':
x = 20 or x = -42
Since we are looking for positive even numbers, the value of 'x' cannot be negative. Therefore, 'x' is equal to 20.
Hence, the consecutive even numbers are 20 and 22, in ascending order.
So, the numbers are 20 and 22.