Olympiad Mathematics | A Wonderful Maths Olympiad Algebra problem |

Added: 2026-05-12

[00:00:00]Hello everyone. Welcome to Rasa's Classroom. Today we are solve a cubic equation which is m to the power 3 + m to the power 2 is equal to 1/8 m is equal to what? How to solve this interesting math question? So our math solution First of all, I take our question which is m to the power 3 + m to the power 2 is equal to 1/8.

[00:00:29]This is our question.

[00:00:32]Now, at this moment if I multiply both side by 8, so it will be 8 * m to the power 3 + m to the power 2 is equal to 1/8 * 8.

[00:00:49]Then this is 8, this is 8, both are cancelled. We are find out which is 8 m cube + 8 m square.

[00:01:01]Then this is 1.

[00:01:04]Now, at this moment you can say this expression this 8 m cube which is 2 m bracket power is 3. Because of that 2 to the power 3, this is 8. m to the power 3, this is m to the power 3. Plus and this expression you can see the little bit 2 * 2 m bracket power is 2 - 1 is equal to 0. I move on this one in this side it will be -1. But at this moment this 8 I take here is 2 * 4. This 4 because of that 2 to the power 2, this is 4. 4 * 2, this is 8 and this is m square. So this expression and this expression both are same.

[00:01:49]Now you can say easily this is 2 m, this is 2 m. So [snorts] let 2 m is equal to T. Now, I substitute this value here.

[00:02:03]So, this expression it will be T to the power 3 then plus 2T squared minus 1 is equal to 0.

[00:02:17]T to the power 3 plus 2T squared minus 1 is equal to 0.

[00:02:22]Now, in this cubic equation you can say here T to the power 3 2T squared which is T to the power 2 plus T to the power 2 minus 1 is equal to 0. T to the power 2 plus T to the power 2, this is 2T squared.

[00:02:40]Then at this moment uh I can say here is T squared, this is T to the power 3. So, T squared is common. So, if I take T squared is common, so this divide this, this is T and this divide this, this is plus 1 plus and in this expression you can say this is A squared minus B squared. So, which is A plus B times A minus B.

[00:03:06]According to this identity, you can say that this expression it will be T plus 1 times T minus 1 is equal to 0.

[00:03:17]Then, this is T plus 1, this is T plus 1. Both are same, so I take here is T plus 1 is common. So, T plus 1 is common. So, if I take T plus 1 is common, so this divide this, this is T to the power 2 and this divide this, it will be T this this cancel, it will be minus 1 is equal to 0.

[00:03:41]Now, we are find out here is two case.

[00:03:43]Our first case which is T plus 1 is equal to 0 and others case which is T to the power 2 + t - 1 is equal to 0.

[00:03:57]We have find out a nice quadratic equation.

[00:04:01]Then, this is t is equal to -1. I just move on this one in this side, it will be -1.

[00:04:09]But here is t is equal to what? So, at this moment, you can say here t is equal to -b + the square root b ^ 2 - 4 ac over 2a.

[00:04:25]If I apply this quadratic formula here, so this t, it will be -b. B is -1.

[00:04:32]Then + - the square root b ^ 2. I mean 1 ^ 2 - 4 ac. A is 1 and c is -1.

[00:04:41]Over 2a. A is 1.

[00:04:43]Then this is t is equal to -1 + - Then this is a square root 1. Minus minus, this is +4 over 2. Now, this is t is equal to -1 + - square root 1 + 4. This is 5 over 2.

[00:05:04]So, we have find out our final answer which is t is equal to -1 and t is equal to this.

[00:05:14]Now, remember that or recall, we have substitute t is equal to 2m.

[00:05:20]So, I take this value here.

[00:05:23]So, t is equal to 2m.

[00:05:25]2m is equal to -1.

[00:05:28]Then if I divide both side by 2, we have find out m is equal to 1/2. So, our final answer which is m is equal to half. But this is 2m. I take this t equal to 2m. This equal to -1 + - the square root 5 over 2. Now, if I divide both side by 2, we are find out m is equal to minus 1 plus minus square root 5. 2 * 2, this is 4. So, our final answer, which is m1 is equal to this and m2 and m3 is equal to this. So, this is our final answer in this interesting cubic math equation. This is the value of m. Thank you all. If you enjoyed this math problem, please subscribe my channel for the next interesting video.

[00:06:16]Goodbye.