Dùng Hằng Đẳng Thức để tìm giá trị lớn nhất p1

Hello everyone, now we will move on to the content of using equations to find the greatest value. In this example 1, I have 3 ideas. We will go to each idea together. The first is the most favorite idea. Last time, we went to find the smallest value, right? Now we will go back to the idea. Now I will go back to the equation of finding the smallest value. Let's see what happens. Now I will have the letter i. I will change the symbol, right? It will be x square minus 2x minus 5. This is the smallest value of the letter i. This letter i is very familiar, we will do it very quickly. The letter i will be equal to x square minus 2x plus 1. Plus 1, the teacher must subtract 6 because we have minus 5. The letter i will be equal to x square minus 1 minus 6. It's very familiar here, right? We see that the letter i is greater than 6. We can explain that because x square minus 1 is greater than 0. We get that the letter i is greater than 6. So what will happen to i? The letter i is greater than 6, so i will be less than 6. i is less than 6, so the teacher will get that i is equal to 6. There is a symbol here, which is the letter i. I will explain it. The letter i is how to write the greatest value of i. We have to point out when. When is the letter i equal to 6? Let's erase this part. When x is equal to 1 square minus 0, the teacher gets x equal to 1. This is a very good way to find the greatest value. Instead of looking for the greatest value, we will look for the smallest value of the letter i. This way is very simple. By transferring, we can find the greatest value of the previous equation. In addition to this, there is another way. I will guide you. Then you will choose the way that suits you. This way will follow the second way. It will follow the theory of designing the letter i by a number m minus a square. For example, i will be less than or equal to 2. Let's erase this part. So now we will use the second way. First, I put the minus sign outside. Inside will be x square minus 2x. To create the equation, I need to add 1. When adding 1, we have minus 1. At first I had 5. So I need to add 6. So our i will become 6 minus x minus 1 square. Now we have x minus 1 square is greater than or equal to 0. 6 minus x minus 1 square is less than or equal to 6. And we get that i is less than or equal to 6. It's the same, right? It's fast, we have to be fast. So the greatest value of i is 6. When x minus 1 square is less than or equal to 1. That's it. So there are two ways. And you can see that the second way has a limitation. For the second and third questions, it will not be as flexible as the first way. For the first way, we only need to replace the minus sign. I will introduce both ways. If you are familiar with it, you can use it. Now we will go to question 2. And I will use the first way to do it. I will write the idea again. To find the value of i, we need to find the min of i. That's the idea. Question 2. I have i equal to 9x square plus 12x plus 2020. First, we convert i to i. The right side will change the sign. It will be 9x square minus 12x minus 2020. Then, minus i will be equal to... We have been prepared from the previous lesson, right? We will see that 9x square is 3x. All square. To create the equation, I will write 12 as 2 times 3x. We have 12, so this is 6. We need to multiply by 2 plus 4 to create the equation. If we write it exactly, it will be 2 square. Plus, we have to subtract. I subtract 2 square minus 2020. To find the value of i, we need to find the value of 3x minus 2 square minus 2024. We have been prepared from the previous lesson, right? We have 3x minus 2 square is greater than 0. So, 3x minus 2 square minus 2024 is greater than minus 2024. I will get minus i is greater than minus 2024. I will get i is smaller than 2024. We have been prepared from the previous lesson, right? When i is smaller than 2024, we will get... I will write it here. We will get minus i is greater than minus 2024. When 3x minus 2 square is greater than 0. I will get x is greater than 3 divided by 2. 2 divided by 3. I will write it on the board. I will write it here. Minus i is greater than minus 2024. When 3x minus 2 square is greater than 0. I will get x is greater than 2 divided by 3. Alright. You can imagine that the biggest value is still the smallest value, right? When we do it, it will be easier and more familiar. Alright. Let's go to number 3. You can imagine that numbers 1 and 2 correspond to the smallest value. First, it is x square. Second, the number is square, right? Let's go to number 3. You will see that the number is 5. It corresponds to the number that is not square. How do we do it? i is equal to minus 5x square minus 6x plus 13. The first step is to convert it into i. To find the smallest value of i. I will convert it into 5x square plus 6x minus 13. You can imagine that when the odd number is not square, we multiply it to make it even. In this case, it is 5x square. I need to multiply it by 5, right? Minus i. I multiply it by 5. It will be 25x square plus 30x minus 65. Do you know what I am missing here? Minus 5, right? Minus 5. Right? Up to here, we will create the equation. This guy will be 5x square. I will divide 30 by 2 times 5x times 3. So I need to add 3 squares to create the equation. Add 3 squares, we have to subtract. Minus 65. Minus 5i equals 5x plus 3. All squares. Minus 3 is minus 9. Minus 9 minus 65 is minus 74. We will do it quickly, right? Bigger than minus 74. Because 5x plus 3 is bigger than 0. So I will have minus 5i. Bigger than minus 74. I get i will be smaller than 74.5. Right? And I will get max i. The largest value of i is 74.5. When. We can do it again. When. When is it? Is it when 5x plus 3 is equal to 0? Let me write it down. 5x plus 3 is equal to 0. So 5x plus 3 is equal to minus 3.5. You can write it down. It is equal to minus 3.5 here. This is the way to do it again. You can use it. Through 3i, the largest value will not be difficult when we switch from the largest value algorithm to the smallest value algorithm of the letter i. You pay attention to this way. See you in the next video. This is part 1. We still have the next parts.