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. The difference of the squares of two positive consecutive odd integers is 32. Find the integers.

Accepted Answer

Hello, everyone in this video, we're going to be looking at this practice problem where we want to find Two positive consecutive odd integers whose difference of their squares is 48. So in this case, I have two unknown numbers where I can say X and X Y, but having two variables is not going to help me figure out what they are. So I'm going to try to relate the two numbers together. So I'm gonna say one number is X and I know that they're related because there consecutive odd integers. So that means that I have my first odd integer and then there's an even integer and then the second odd integer. So that means that my second integer is X plus two because if I go to, to the right, I reach my next odd integer. So now I have defined both of my integers using the same variable X where X will be one of my integers. And in order to find My second one, I just need to add to two X. But now let's see what the problem is saying About their square. So it's saying the difference of their squares is 48. So difference means subtraction. So I have x plus two squared because difference of their squares -X Squared is equal to 48. And now I need to solve for X. So I'm going to expand this exponent. So I have X plus two times X plus two minus X squared is equal to 48. I do foil method. I have X times X is X squared, X times two is two, X again, two times X is two, X and two times two is four. I can combine the middle terms. Two, X plus two, X is for X minus X squared, some positive X squared minus X squared leaves me with zero. So I'm left with four, X plus four equals 48. I'm still trying to isolate X here. So I'll subtract four from both sides. So it leaves me with four. X is equal to 48 minus four, Which is 44. And in order to Electricly isolate x all divide both sides by four. So it leaves me with X is equal to 44 divided by four, which is 11. So 11 is one of my integers. And I said that the second integer would be X plus two or 11 plus two. So 13. So that means that my two integers are 11 and 13. And if we look at the answer choices, You can see that answer choice D also has 11 and 13. So hopefully this video helped and see you next time.

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