The product of two consecutive positive even numbers is 1368. What are the numbers? (Enter solutions from smallest to largest.)

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The square root of 1368 is almost 37.

What is the product of 36 and 38?

Well, to find the consecutive positive even numbers that would have a product of 1368, we can use some detective skills. Let's start narrowing it down!

First, we know that the product of the two numbers is 1368. So, let's play a game of multiplication charades.

Let's say the first number is x. That means the second number would be x+2, since they are consecutive even numbers.

Now, if we multiply these two numbers together, we should get 1368. So, we have the equation x * (x+2) = 1368.

Let's solve it together. Get your detective hats on!

Let's assume the two consecutive positive even numbers as x and (x+2).

According to the given information, the product of these two numbers is 1368.

So, we can write the equation as:
x * (x + 2) = 1368

Expanding the equation:
x^2 + 2x - 1368 = 0

To solve this quadratic equation, we can factorize it or use the quadratic formula.

Factoring the quadratic equation:
(x - 34)(x + 40) = 0

So either (x - 34) = 0 or (x + 40) = 0

If x - 34 = 0, then x = 34
If x + 40 = 0, then x = -40 (This cannot be one of the positive even numbers)

Therefore, the two consecutive positive even numbers are 34 and 36.

The solution is: 34 and 36.

To find the two consecutive positive even numbers that have a product of 1368, we can use algebraic equations.

Let's assume the first even number is represented by x. Since the numbers are consecutive, the next even number will be x + 2.

The product of these two numbers can be expressed as:
x * (x + 2) = 1368

Now, let's solve this equation to find the values of x and x + 2.

Expanding the equation, we have:
x^2 + 2x = 1368

Rearranging the equation, we get:
x^2 + 2x - 1368 = 0

To solve this quadratic equation, we can use factoring or the quadratic formula. In this case, factoring might be simpler.

The quadratic equation can be factored as:
(x + 38)(x - 36) = 0

Setting each factor equal to zero, we find two possibilities:
x + 38 = 0 ==> x = -38
x - 36 = 0 ==> x = 36

Since we are looking for positive even numbers, we discard the negative solution x = -38.

Therefore, the first even number, x, is 36. And the next consecutive even number is x + 2, which is 36 + 2 = 38.

Hence, the two numbers are: 36 and 38.