Answer each question. Answer each question. Answer each question....

Question

Answer each question. Answer each question. Answer each question. Unknown NumbersUse the following facts.If x represents an integer, then x+1 represents the next consecutive integer.If x represents an even integer, then x+2 represents the next consecutive even integer.If x represents an odd integer, then x+2 represents the next consecutive odd integer. Find two consecutive even integers whose product is 168.

Accepted Answer

Hey, everyone in this problem, the product of two consecutive even integers is given us 360. And we're asked to find those two integers. Now our answer choices are a 18 and 20 B negative 20 and negative 18 or 18 and C negative 18 and positive 20 or D negative 20 and positive 18. Alright. So let's think about this. We have the product of two consecutive even integers. Okay. So let's let X be the first integer. Hmm Well, the consecutive even integer is then going to be X plus two Because we're talking about even introduce the difference between the two will be two. Okay. So we have X, our first value X plus to our second integer and we know that the product of them is going to be 360. So we have the X times X plus two is going to be equal to 360. Now let's go ahead and expand. We're going to have X squared plus two X. Okay. We need to distribute this X to both the X and the plus tutor Is equal to 360. We can subtract the 360, we have that X squared Plus two, X -360 is equal to zero. Hey, we factor this can factor. Anyway, we would like we see that X minus 18 Times X-plus 20 is equal to zero. Alright, so if we solve for X okay, we have a Term multiplied by another term equal to zero. So if either of these terms are zero, then the left hand side will be zero and the equation will be satisfied. And so from the first term we get that X is equal to 18, then from the second we get that X is equal to negative 20. Alright. So we have two possible solutions 18 and negative 20. Let's start with the first, if X is equal to positive 18, then X plus two is equal to 18 plus two which is equal to 20. Okay. So we have 18 and 20 is a solution. Those are two consecutive even integers. Okay? And when we multiply them, we get 360. Now if X is equal to negative 20, then X plus two is equal to negative 20 plus two which gives us negative 18. Okay. So we have negative 18 and negative 20. Those are also two consecutive even integers. And when we multiply them, we also get 360. And so we actually have two solutions 18 and 20 as a solution and negative 18 and negative 20 is a solution. So we look back at our answer choices and we see that this corresponds with answer choice B we have negative 20 and negative or 18 and 20. That's it for this one. Thanks everyone for watching. See you in the next video.

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