Le plus grand piège des Olympiades de maths

Ladies and gentlemen, do you find it normal that we give these kinds of equations in the mathematical olympiads? I can tell you that it's a trap. x plus 11 which is equal to x that we are asked to solve. So, we just need to say that x, here, the x is in place. This x, I move it to the other side and it will become minus x which is equal to minus 11. That is, even the plus 11, I move it to the other side. I just regroup the x on one side and the numbers without x on the other side. So, x minus x gives us 0. 0 is equal to minus 11. So, we ask ourselves the question, 0, is 0 equal to minus 11? 0 is not equal to minus 11. So, that's impossible. That is, our equation has no solutions. But there are other alternatives. Here, if we want to get the value of x, the x disappears. You see? So, when the x disappears, we will judge if the number on this side of the equality is equal to the number on the other side of the equality. That is, if we find 0 equals 0 or 11 equals 11 or minus 11 equals minus 11, then we will say that the set of solutions is R. Which means that any number you take can be a solution to our equation. But here, this is not the case. We found 0 here and 11 on the other side. When the numbers you find on this side and on the other side are different, that is, there are no solutions. So, 0 is different from minus 1. There are no solutions. But we will look for another alternative to solve this equation. So, there is a rule that says that there are no solutions S together 8. We have x plus 11 which is equal to x. x plus 11 equals x. So, what are we going to do? There is a rule that says that if a equals b, it means that a squared is also equal to b squared. If x plus 11 is equal to x, it means that x plus 11 squared is equal to x squared. You see? So, we are going to develop this. We are going to develop x plus 11 squared. So, we are going to say that x plus 11, the factor of x plus 11, which is equal to x squared, is equal to x squared. Now here, x times x gives us x squared plus x times 11 gives us 11x plus 11 times x gives us 11x plus 11 times 11 gives us 121 which is equal to x squared. So, let's arrange this first. We will have x squared plus 11x. plus 11x gives us 22x plus 121 which is equal to x squared. Now, I am going to move the x squared to the other side of the equation. So, I am going to have x squared minus x squared plus 22x plus 121 equals 0. So, x squared minus x squared will simplify. I am going to have how many here? I am going to have 22x plus 121 which is equal to 0. Now, we move the 121 to the other side of the equation. So, 22x is equal to minus 121. So, we have to subtract x. x is equal to minus 121 divided by 22. Now, x is equal to minus 121. It is 11 times 11 which gives us 121. And 22 is 2 times 11 which gives us 22. So, we simplify here. 11, 11. We are going to have x which is equal to minus 11 over 2. Now, let's see. Can minus 11 over 2 be a solution to our equation? If you have reached this point, don't forget to like the video and subscribe. So, we are going to do a verification. Verification. So, the verification. We have x plus 11 which is equal to x. We replace where there is x by minus 11 over 2. Minus 11 over 2, sorry. Minus 11 over 2 plus 11 which is equal to minus 11 over 2. Does it give us minus 11 over 2? So, we reduce to the same denominator here. We will have 1 times minus 11 which is minus 11 plus 2 times 11 which is 22. All over 2 times 1 which gives us 2 which is equal to minus 11 over 2. Minus 11 plus 22. How much is it actually? Minus 11 plus 22 is 11. Is 11 over 2 equal to minus 11 over 2? 11 over 2 is not equal to minus 11 over 2. To tell you that when you have a equals b, it doesn't mean that a squared is equal to b squared. If it were the case, we would find a solution. This works when you have the absolute value of a is equal to the absolute value of b. This is what gives a squared is equal to b squared. So, if it was an absolute value, let's see how to solve it and how to find the solution. So, if you've made it this far, don't forget to ask your questions in the comments. I would be happy to answer them with a video. So, if we have x plus 11 equals x and that it was an absolute value, here we agree. Here we agree that you raise both terms to the square. That is, you will have x plus 11 raised to the square is equal to x raised to the square. And here, when we check, it will check because here we will have the absolute value of minus 11 over 2 which is equal to 11 over 2. And the absolute value of minus 11 over 2, here we found 11 over 2, here we found minus 11 over 2. Here, in this case, 11 over 2 in absolute value gives us 11 over 2. And minus 11 over 2 in absolute value also gives us 11 over 2. So, if you liked the video, don't forget to share it, like it and subscribe to the channel so you don't miss our next videos.