Tricky Algebra math question.

Hello wonderful people, you are welcome back to my channel. So today we are asked to find the value of x and y in this Harvard interview question. Now this is very tricky. First of all, recall that a squared minus b squared is equal to a minus b multiplied by a plus b. Okay? Therefore, we can rewrite this as x minus y multiplied by x plus y is equal to 35. Now, we need to check something. If this is positive, right, it simply means that x is greater than y, right? Yes. Also, x plus y is greater than x minus y. because here you are adding to x and here you are taking away from x so definitely x plus y is greater please subscribe to my channel turn on your notification bell if this is the first time you are coming across my video give me a thumbs up if you love what i'm doing and always comment yes tell me what you feel about the video the good the bad the ugly just tell me in the all right now back to what we are doing what does this mean now recall that let's list all the factor pairs of 35 now 35 is the same as 1 multiplied by 35 35 multiplied by 1 7 multiplied by 5 5 multiplied by 7 so we have four possibilities here now but you are going to reduce them based on these things that we noticed so we noticed that x plus y is greater than x minus y so if my if i should write this equation as x plus y multiplied by x minus y is equal to 35 so it means that this will be deleted and this will be deleted so we'll be using this and this right so we have two trials here or two cases case one or the first case we have 35 multiplied by one as we are going to replace this with this so we are going to have x plus y multiplied by x minus y is equal to what 35 multiplied by 1 now stay till the end because you're going to see at the end of the video i'm going to prove that the answer we got is correct so ensure that you watch to the end okay so we have this from here x plus y is 35 right Let's call this equation 1. Then x minus y is 1. Let's call this equation 2. Now, let's add plus x is 2x. y minus y is 0. 35 plus 1 is 36. So, to get the value of x, let's divide both sides by x, by 2, rather. So, this, we go into this, and we have x is equal to We go into this 18. So, we have the first value of x as 18. That is our x1. Now, from this first equation, or let's use the second equation. From the second equation, we have x minus y is 1. 18 minus y is 1. So, if we bring this to this side, we have 18 minus 1 is equal to, and minus y goes to the other side to become plus y. So, 18 minus y is 17. So we have 17 is equal to y. So that means our y1 with x1 is 18, y1 is 17. Remember, we're going to prove if this is correct or wrong. Now for the second case, case 2, for the second case, we have x plus y multiplied by x minus y is what? It's going to be 7 times 5. So, we have x plus y is 7, equation 1. x minus y is 5, equation 2. Now, we add x plus x is 2x. This is 0, is equal to 7 plus 5 is 12. Now, to get x, we divide both sides by 2. Divide it by 2, divide it by 2. This, we can see this, we have x is equal to 6, okay? So, we have our x2 to be 6. Now, let's find the corresponding value of y. From equation 1, we have x plus y is 7, right? So, our x is 6, 6 plus y is 7. So, if we bring this, okay, let's take this to the other side so that we don't have a negative. So, we have y is 7, take away 6, and y is 1. So, y2 is equal to 1. Now, let's prove that the answer we got is correct. So let's check. The equation says that x squared minus y squared is 35. So let's pick the first values of x and y. So x1 is 18, 18 squared. Y is 17, 17 squared is 35. Now, 18 minus, this can be written as 18 minus 17 multiplied by 18 plus 17 is 35. So, 18 minus 17 is 1. 18 plus 17 is 35, is equal to 35. So, from here, you can see 35 is equal to 35. That means that this is correct. So, we have checked the first answer. Let's check the second one. For the second set of equations, we have x2 is 6, 6 squared, and y2 is 1 squared, is 35. 6 squared is 36, 1 squared is 1. So, it's obvious that this is 35. Thank you so much for watching and see you in my next video. Bye.