the product of two even consecutive integers is 224. find the integers
To find the two even consecutive integers whose product is 224, you can use a systematic approach. Let's call the first even integer "x" and the next consecutive even integer "x+2".
Step 1: Set up an equation
According to the problem, their product is 224. So, we can write the equation:
x * (x+2) = 224
Step 2: Solve the equation
To solve this quadratic equation, we will simplify it and then solve for "x".
x^2 + 2x = 224
Rearrange the terms:
x^2 + 2x - 224 = 0
Now, we can either factor this quadratic equation or solve it using the quadratic formula.
Let's factor it:
(x + 16)(x - 14) = 0
Now, we set each factor equal to zero and solve for "x":
x + 16 = 0 OR x - 14 = 0
Solving for "x" in the first equation gives:
x = -16
Solving for "x" in the second equation gives:
x = 14
Step 3: Find the consecutive even integers
Since we are looking for even integers, we need to check if "-16" and "14" are even.
-16 is even, and so is 14.
Therefore, the two even consecutive integers whose product is 224 are -16 and 14.
Let the two integers be
(x+1) and (x-1), the product is therefore
N=(x+1)(x-1)=x²-1
therefore
x=√(N+1)=√(224+1)=√225=15
The two integers are 15+1 and 15-1, or 14 & 16