Olympiad Mathematics | India | Can You Solve This One?

Added: 2026-05-24

[00:00:00]You are welcome back to our YouTube channel. In this video, you want to find the value of B given that you have this problem. Then let's have it be solution.

[00:00:11]So we have to find B. This is B * B * B.

[00:00:15]This will give us B to the power of T equals B + B + B. So we are going to add this together. This will give us TDB.

[00:00:26]If we divide through by b this will reduce one of the solution of this problem. So we are not going to do that.

[00:00:33]Let take this 3 b to this side and set this side to be equal z. So we are going to have the complete solution. So we have b to the^ of 3 minus 3 b = 0.

[00:00:47]Then from here what is common between b ^ 3 and - 3 b is b. Factor it out. We're going to have three sorry b outside b to the^ of 3 / b this will be b to the^ of 2 left minus by plus here will be minus 3 b / b from here we have it to be 3 = 0.

[00:01:12]Now from here what we are saying is that is very simple for this side we have it to be zero. This is either we have b to be equals z or we have this to be equals z. And in that case we are going to apply zero product rule and that six is either we have b to be equals z. We already have one solution or we have b to the power of 2 b ² - 3 = 0. Now let us now recall that when we have a equ= as a to the power square root of a².

[00:02:09]So from here we can apply it here because we have this to be the first solution. We can apply it here. meaning that we're going to have here to be b to the power of b² minus square<unk> of 3² = 0. Now from here we can apply difference of two square that is when you have x² - y² = x + y * x - y.

[00:02:40]So from here we are going to have this as we have b + <unk>3 * b - <unk>3 = z. By apply zero product law again it's either we have b + <unk>3 = 0 or we have b - <unk>3 = 0.

[00:03:14]And so from here by taking this 3 + 3 to this side. So definitely we're going to have this to be b = -<unk> 3. And from here taking this one to this side it will be b equals + 3. So we have the value of b we can declare value of a and for value of b to be equals z can say b1 then b2 = -<unk>3 then b3= + <unk>3.

[00:03:56]So having got this one as we have it here there's need for us to check to check the solution.

[00:04:09]So check it we have b * b * b you say = b + b + b.

[00:04:20]So from here this will be 0 * 0 * 0. Question now is is it going to be equ= 0 + 0 + 0. Now from here 0 * 0 * 0 will give us 0. Then 0 + 0 + 0 will give us 0. So we have this to be 0= 0 satisfied.

[00:04:46]And the reason is that the left hand side equals the right hand side. Let test for B2 that equals minus <unk>3.

[00:04:55]From the above we have -<unk>3 * -<unk>3 * -<unk>3.

[00:05:03]Then is it going to be equals - <unk>3 - <unk>3 -<unk>3 minus * minus will be + <unk>3 * <unk>3 will be <unk>3² * -<unk>3 -<unk>3 -3 will be - 2 <unk>3 - <unk>3.

[00:05:31]So from here we have plus * minus will be minus this will cancel out this we have this here to be take left we have here * this will be -<unk>3 then from here - 2<unk>3 - <unk>3 will give us -3 <unk>3 so from here one can see clearly that the left hand side equals to the right hand side and if that's to be the case this also satisfied.

[00:06:10]Now we also have to test for B3 that equals <unk>3.

[00:06:24]So definitely this will be b * b * b = b + b + b. So this will now be <unk>3 * <unk>3 * <unk>3. Then is it going to be equals <unk>3 + <unk>3 + <unk>3 <unk>3 * <unk>3 here we have <unk>3² * <unk>3 then is it going to be equals this will be <unk>3 + roo<unk>3 will be 2<unk> 3 + <unk>3 now this square root and square will cancel out. This will cancel out this.

[00:07:18]So we have 3 * <unk>3.

[00:07:24]Then from here is going to give us + 2<unk>3 + <unk>3 will give us 3 <unk>3.

[00:07:36]One can see clearly that this left hand side equals to to this right hand side as well. So if that to be the case, this also satisfied.

[00:07:46]One can now declare finally that our B = Z, B1, then our B2 equals