Answer each question. Answer each question. Unknown NumbersUse th...

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 integers whose product is 110.

Accepted Answer

Everyone. Welcome back in this problem. We're told that the product of two consecutive integers is 90. And we're asked to find the two integers. And our answer choices are a negative 10 and negative nine B nine and 10, C negative 10 and nine or de negative 10 and negative nine or nine and 10. Now we're talking about the product of two consecutive integers. Okay. So if we let X be the first integer, then X plus one is going to be the second integer. Okay, we're talking consecutive integers. So we just add one to get the next integer. Now we know that the product of them is eight is 90. Okay. So this tells us that X times X plus one is equal to 90. Let's expand on the left hand side. So we distribute the X to both the X and the plus one term. So we have X squared plus X is equal to 90. Okay. And we'll recognize this now as a quadratic And we want to set one side equal to zero so that we can solve just like we do all the time. So let's move the 90 to the left hand side, we're going to have X squared plus X minus 90 is equal to zero. And we can solve for X in a couple of different ways. We could use the quadratic formula at this point. We can also factor. And so this looks fairly nice to factor. Let's go ahead and factor And we get the factors X - times X plus 10 is equal to zero. Okay. If we were to expand this, we get X squared plus 10, X minus nine, X plus 10, X minus nine, X gives us X like we have and then we have negative nine times 10 which gives us our negative 90. Alright. So We have two terms multiplied together that equals zero. If either of those terms is zero, the entire left hand side will be zero and this equation will be satisfied. And so we get the possible x value from the first term of nine And a possible x value from the second term of -10. Alright. Let's start with the first one. If X is equal to nine, then X plus one is equal to nine plus one is equal to 10. OK? So are integers are nine and 10. Those are consecutive integers. Okay? And when we multiply them together, we get 90. So those do indeed satisfy this condition. Okay? So we have at least one solution. Let's not forget to look at -10 as well. If X is equal to negative 10 than X plus one is equal to negative 10 plus one Which gives us -9. Yes, we have negative nine And negative 10. Those are consecutive integers. And if we multiply them together, we also get 90. And so this is also a solution. And so the answer here is going to be D we can have negative 10 and negative nine or nine and 10. Thanks everyone for watching. I hope this video helped see you in the next one.

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