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 even integers is 84. 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 even integers whose difference of their squares is 124. So in this case, we have two numbers to unknown numbers. So I can say are X and Y and the difference of their squared. So I'll say Y squared, the second unknown number minus the first unknown number squared is equal to 124. Well, in this equation, you can see that we have two unknown variables. So we can't really solve for either one of them. So I am going to try to relate my two variables together. So they can be my two unknown numbers together so that I can use one variable to solve for them. So in this case, I know that they're consecutive even integers. So because they're consecutive even integers, I know that I have my first number. So you draw a number line, my first even number, then there's an odd number and then my second even number. So you can see that between my two consecutive numbers is two units. So I can say that my first number is equal to X and my second number is equal to X plus two. So in this equation, I can replace Y with X plus two. And now I only have the X variable that I'm solving for. So I can go ahead and solve for X. I'm going to expand this exponent on the left hand side. So I have X plus two times X plus two minus X squared is equal to 124. X times X is X squared, X times two is two, X, two times X is two X and two times two is four minus X squared. Still equal to 124. You can see that I have a positive X squared and a negative X squared. So those cancel out or eliminate each other. I can combine my middle terms. I have two X plus two, X is four, X. So I'm left with four, X plus four is equal to 124. And I'm still trying to solve for X. So I'll subtract four from both sides. So it leaves me with four, X is equal to 1 24 minus four is 1 to completely isolate X all divided by four. So that leaves me with X is equal to 30. So that means that one of my numbers is 30 and I said my second number would be 30 plus two. So my second number is 32, 30 and 32 are my consecutive even integers. Who's difference of their squares is 124. And if we look at the answer choices, you can see the answer choice. B also has 30 and 32. So hopefully this video helped and see you next time.

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