Germany | Can you solve this ? | Maths Olympiad

Añadido: 2026-05-26

[00:00:00]Hello, you are welcome to solve this math problem which is B + B + B is equal to B * B * B. To find the values of B from this equation now solution into the left side B + B + B it is 3 B is equal to in the right side B * B * B it is B power of 3. Then in the next step we exchange we take this b^ power three in the left side and 3 b to the right side. So we start by this b^ of 3 is equal to this 3 b. Then we take 3 b to the left side. So it will be b^ 3. This take this side will be min - 3 b is equal to zero.

[00:00:56]Now into here b is common. So we take b outside the bracket b^ 3 / b it is b² then minus 3 b / b it is 3 bracket is equal to zero.

[00:01:12]Then from here we have two solutions where this first solution of b is equal to zero. So this is the first value of b and the second solution it is b² - 3 is = 0. Then into here it will be b² - 3 make into square.

[00:01:38]Now from a example of the rule a is equal to square roo<unk> of a square. So three here three it will be equal to square<unk> of 3 squared. So into three we substitute this. So here it is square<unk> of 3² it is 3 is = 0. Now into here it is now in the form of difference of two squares. So we'll apply difference of two square rule which is x² - y² is = x - y bracket bracket x + y bracket then we'll apply this form x - y it will be b - 3. So b -<unk> of 3 bracket then bracket x + y it will be x b it will be b + 3. So here b + t of 3 bracket is equal to zero.

[00:02:43]Then into here we have two solutions where this first solution of b minus roo<unk> of 3 is = 0 and we have this solution b +<unk> of 3 is = 0. Then here I take roo<unk> of 3 to this side. So it will be b is =<unk> 3. So this is the other solution. Here I take roo<unk> 3 to this side. So it will be b = -<unk> 3. Then this is the other solution or from here into this step here b ² - 3 = 0. So from b² - 3 is = 0. We take -3 to this side. So it will be b² is = 3. Then we apply square root in both sides. So it will be square root of b square is = square roo<unk> of 3.

[00:03:43]Now into here this square root you cancel square then it will be b is = to plus or minus square roo<unk> of 3.

[00:03:51]Whereas here it is this when it is positive b is roo<unk> 3 when it is negative it is minus 3. So our conclusion the first value of B is equal to this zero.

[00:04:07]The second value of B is equal to square<unk> of 3. And the third value of B is equal to this minus roo<unk> of 3.

[00:04:20]So these are all the values of B from this our problem. Now in the next step let's check these answers if they are correct. So to check for my problem which is b + b + b is equal to b * b * b. Now let's check for first value of b which is equal to z. So here it will be 0 + 0 + 0 is it = 0 * 0 * 0. Now 0 + 0 + 0 is 0 is equal to 0 * 0 * 0 it is 0. So left side and right side are equal then it is true for first of b is equal to z.

[00:05:07]Now let's check for the second value of b. So here we check for second value of b is square root of 3. So here we substitute square root of 3. So it will be square<unk> of 3 +<unk> of 3 +<unk> 3 is it = to square<unk> of 3 *<unk> 3 * square<unk> of 3.

[00:05:32]Now into here roo<unk> 3 is common. So we take roo<unk> of 3 outside the bracket. Now 3 /<unk> 3 it is 1 plus 3 * 3 is 1 + 3 / 3 it is 1 bracket is it equal to from here 3 * 3 it is 3 then times this<unk> of 3. Now here we add 1 + 1 + 1 it is 3 * this<unk> of 3 is equal to 3<unk> 3. So left side and right side are equal then it is true for second of B is roo<unk> 3.

[00:06:16]Now let's check for the third value of B is equal to<unk> of 3.

[00:06:25]So into here into B + B + B we substitute this. So it will be -<unk> 3 then + -<unk> 3 then + -<unk> 3 is it = b * b * b it will be -<unk> 3 * -<unk> 3 * -<unk> 3 so into here - 3 is common so we take - 3 outside the bracket now - 3 - 3 it is 1 plus this / this is 1 plus this / this is 1 bracket is equal to - 3 * - 3 it is positive - * - is positive 3 * 3 it is 3 then times this here - 3 so here -<unk> 3 then here we Add 1 + 1 + 1 it is 3. Then time this here - 3. So here it will be -<unk> 3 is it is equal to 3 * this - 3 it is - 3<unk> 3. So left side and right side are equal. Then it is true for the val of the third val of b is minus root of 3. So already check for these three solutions. So this is the correct solution.

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[00:08:11]Bye-bye. Bye.