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 odd integers whose product is 63.

Accepted Answer

Hello, everyone. In this video, we're going to be looking at this practice problem where we want to find two integers whose product is to introduce that are odd, whose product is 99, they're also consecutive integers. So in this case, we have to unknown integers that when we multiply them together, their product is 99. But you can see that in this equation, I have two variables X and Y. So I denoted my first integer, X and my second integer Y, but having two variables won't help me solve what the integers are. So I want to try to relate the two. So when you think of a number line, we have an odd number followed by an even number and then an odd number again, which means that odd numbers are two units apart. So that means if my first number is X, my second number would be X plus two. So if I plug that in to my equation here, I have X times X plus two, I'll distribute this X. So I have X squared plus two, X is equal to 99. And now I'm going to move the 99 over to the left hand side by subtracting. So I have X squared plus two X minus 99. You can see that this is a quadratic equation. So I'm going to try to solve X by factoring. So I want to find two factors. And the first term needs to multiply, the first terms need to multiply two X squared. So I can do X times X is X squared. And I need the last terms to multiply to give me negative 99. So when I think of factors for -99, I could have negative three and positive 33 or the vice versa And could have nine times negative 11 or the opposite positive 1 -9. So for this factor, I'm going to start by trying X minus nine and X plus 11 and I can check this really quick by foiling. So I have X times X is X squared, negative nine times X is negative nine, X X times 11 is positive 11, X and negative nine times positive 11 is negative 99. So in this case, this becomes X squared negative nine, X plus 11, X is two X minus 99. You can see that I get the original equation back. So I know that these factors are good, which means that I can have X minus nine is equal to zero or X plus 11 is equal to zero. Solving for X, I'll add nine, which means X could be nine. Again, solving for X, I'll subtract 11 Which means X could be negative 11. So now I have two possible solutions for X which is one of my odd integers. But keep in mind, I still need to consider my second integer. And because X has two solutions, my second integer will also have two solutions. So when X is equal to nine, my second number will be equal to nine plus two Or and one X is equal to -11. My second number will be equal to negative 11 plus two, which is negative nine. So that means that I could have negative and negative nine or nine and 11. So this becomes my final answer for this problem. And you can see that this aligns with answer choice A so hopefully this video helped and see you next time.

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