Olympiad Algebra Tricks They Don’t Teach in School.

Added: 2026-05-17

[00:00:02]You're welcome to this special Olympia math class.

[00:00:06]So, we have find the minimum value of X plus 9 over X.

[00:00:11]Now, this may look very difficult at first.

[00:00:16]But, if you understand the principle behind this, it will be easier.

[00:00:22]All right. Remember on the last part one on trying to illustrate this principle, I say that there are conditions you must apply.

[00:00:32]The first condition is whenever I see this question, you are seeing some then know that there is product inside that. Now, the sum and the product are combined in an a relationship according to AM to GM rule.

[00:00:50]Now, the question is what is AM to GM rule? The rule rule says that if you have two numbers two real numbers which are greater than zero, it says that the sum the average of the sum must be greater or equal to the square root of the product of the uh the product of the numbers.

[00:01:11]So, from this place, the question we are given is X plus 9 over X.

[00:01:17]So, I'm going to apply the same rule.

[00:01:19]So, I'm going to have X plus 9 all over X divide two is greater or equal to the product of X multiply by 9 all over X.

[00:01:33]I'm sure you're seeing what I'm going to be doing there. So, let's simplify the product. So, we have X times 9 all over two.

[00:01:42]Uh not all over two. Let me clean up something there.

[00:01:46]Um So, this is going to be divided by X all divided by two is greater or equal to the square root of nine.

[00:01:57]So, that's going to be x + 9 over x all divided to is greater or equal to three.

[00:02:06]Now, on the next we have x + 9 over x is greater or equal to 2 * 3 is going to be 6. So, you see the minimum value is going to be 6 because x plus 9 over x is going to be equal to 6 and I go on to infinity. Therefore, the minimum value is 6. So, this kind of principle is used to be able to find the minimum value of two real numbers.

[00:02:39]Thank you for being part of this class.

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