Olympiad Mathematics | Indian | Come and solve this.

Ajouté : 2026-05-11

[00:00:00]Hi everyone.

[00:00:03]If you're ready, I am ready. Let's solve this problem here.

[00:00:10]Solution.

[00:00:12]Okay. By the way, we are going to solve this in two ways.

[00:00:18]Let's apply our first method.

[00:00:25]Okay.

[00:00:26]Let's apply our first method very quickly.

[00:00:32]We have the square root of 2b over b equals 5.

[00:00:40]So, the first method is going to involve um cross multiplication.

[00:00:49]Okay.

[00:00:51]From the first step.

[00:00:53]So, we cross multiply. 2b will multiply 1 and that will give us root 2b. Root 2b.

[00:01:01]Root 2b.

[00:01:03]Then it's going to be 5 * um b, which will give 5b.

[00:01:09]Now, the next thing is to remove the square root sign.

[00:01:12]Because as long as the square root sign is there, we can't find the b under it.

[00:01:18]So, we have our root b, I mean root 2b.

[00:01:23]And we square it.

[00:01:25]Now, we have 5b.

[00:01:29]And the whole of that will be squared.

[00:01:32]Do not forget to put that under um the square root sign.

[00:01:37]Because if you don't, the square root will be for b and not for the 5.

[00:01:45]Okay. So, this one and this one are going to go so that 2b is alone and is equal to 5b multiplied by 5 b.

[00:02:00]Okay?

[00:02:02]And now, 2 b is equal to 5 * 5 is 25.

[00:02:09]b * b is b squared.

[00:02:13]But, we are expected to write the one with the higher power first.

[00:02:18]So, we can write 25 Okay?

[00:02:23]We write 25 b squared to be equal to 2 b squared.

[00:02:30]Okay, I did this in my last video, and somebody was of the opinion that since we changed the position of the variables, the position of the terms, that they should become negative.

[00:02:45]Right?

[00:02:46]Now, there's no point having them negative.

[00:02:50]Right?

[00:02:51]There's no point. And And I'm going to explain why.

[00:02:55]Even if you're going to change the position, 25 b squared came to the left, and you want it to become negative.

[00:03:03]Very possible, right?

[00:03:05]And then, this 2 b is going to the right, and you want it to become negative, negative 2 b.

[00:03:14]Right? This is still very correct.

[00:03:17]And what will happen now is that the negative here will take out the negative here.

[00:03:23]Right? So, it will take you back to where you're coming from, and that is your 2 5, you know, 25 b squared to be equal to 2 b on the right. So, you don't have to make it negative or make them negative.

[00:03:39]Now, bring this to the left as you have 25 25 b squared minus 2 b, and this is equal to zero.

[00:03:52]Because nothing on the right-hand side anymore.

[00:03:55]Now, we carry out our factorization.

[00:03:58]B is a common factor.

[00:04:01]Here we have 25 25 B Okay, sorry about that. 25 then this negative is coming down. B is already out, so you write your two.

[00:04:15]And this is equal to what?

[00:04:18]Zero.

[00:04:19]So, from zero product rule B is zero or 25 B minus two is equal to zero.

[00:04:33]Okay, so B is either zero or 25 B minus two is zero.

[00:04:40]And our B here is already zero.

[00:04:43]Here 25 B is equal to two. Negative becomes positive, right?

[00:04:51]And now we divide both sides by 25 from this part.

[00:04:56]But B here is already zero.

[00:04:58]Or B on this side is going to be two over 25.

[00:05:05]Since we are dividing both sides by two.

[00:05:09]So, from the first method we got some We got B to be zero or two over 25.

[00:05:18]Now, don't see anything yet. Let's look at the second method.

[00:05:25]Okay, so we are going to continue from here. The second method. Now, this method is going to be faster and easier for you.

[00:05:38]Yes, that's the more reason I should stay and get the second method. This is 2 B over B equals five.

[00:05:46]Now, remember the first method gave two solutions.

[00:05:50]So, how many solutions do you think this method will give?

[00:05:53]Is it one, two, or three?

[00:05:55]Let's look at it.

[00:05:57]So, the first thing I want to do is to square the left-hand side. So, I'm going to write root 2 B over B.

[00:06:07]This is squared. The left-hand side is squared.

[00:06:11]Okay, we've squared the left and we'll equally square the right.

[00:06:17]So, that this one can take Okay, hold on. Remember that this power is for both numerators, right?

[00:06:24]Okay, it's for both numerator and the denominator. For the numerator, the square root and the square will go.

[00:06:31]So, we have just 2 B for the numerator.

[00:06:35]And then for the denominator, we have B to the power of two.

[00:06:40]That is B squared.

[00:06:42]And this is equal to 25, which is 5 squared.

[00:06:47]I told you it's going to be faster.

[00:06:50]Now, from here, we can even do this. 2 into You know, 2 into B over B over B squared, by the way. You know, the denominator is B squared.

[00:07:05]And this is equal to 25.

[00:07:08]Guess what I will do.

[00:07:10]We can cancel out one B from the denominator. So, 2 will now be multiplied by 1 over B.

[00:07:20]And this is equal to 25.

[00:07:23]I told you this would be faster and easier.

[00:07:26]So, the next point now is to divide both sides by two.

[00:07:31]This will go and then 1 over B on the left-hand side is equal to 25 over two.

[00:07:43]And what are we looking for?

[00:07:46]We are looking for the value of B, not 1/B.

[00:07:50]So, we'll take the reciprocal of the left, which will give us B/1.

[00:07:54]And it is the same as B.

[00:07:57]Okay, it is the same as B.

[00:08:01]And then we'll also take the reciprocal of the right, which will turn to 2/25.

[00:08:07]And if you can remember, this is one of the solutions we got from the first method.

[00:08:14]Okay, the difference between the first and the second method is that the first method gave us two solutions.

[00:08:20]And the second method gave us one solution.

[00:08:25]Let's go back to the equation and see it for yourself.

[00:08:29]Okay, so this is the original equation.

[00:08:32]Our B from the first method is zero or 2/25.

[00:08:38]And from the second method, we only got B to be equal to 20, okay, 2/25.

[00:08:47]Now, if you look at the equation, we're having root 2B/B. So, that means that if you're going to substitute the value of B to be zero, you're having 0/0.

[00:08:59]So, B to be zero cannot satisfy the equation. So, B = 0 will be rejected.

[00:09:08]But the second solution gave B to be 2/25 alone, and B to be equal to 2/25 satisfies the equation.

[00:09:20]So, if I were you, I will apply the second method since it will give me all that I need.

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[00:09:37]Thank you.