This question initially seems very difficult but it is really just testing whether you break down what it is that the question is asking. We are given two numbers, (x-1), x and (x+1). We are also given that the product of the three numbers is five times their sum.
To work out the product we must simplify: (x-1)(x)(x+1). Essentially, we are expanding three brackets. To do this, just expand the first two brackets as you would normally and simplify. Then, expand this new bracket with the remaining last bracket. I have included an image of how to do this below:
Then, we must work out the sum of the three numbers. So we must do: (x-1) + x + (x+1). This is fairly simple and comes out to 3x. However, we are given that the product of the three numbers is five times their sum. Thus we must multiply 3x by 5 to get 15x.
We can now say that 15x is equal to the product of the three numbers, which is x^3 - x in this case. That is the answer to part a.
For part b, we just have to rearrange the equation x^3 - x = 15x by subtracting 15x from both sides of the equation. We will therefore get x^3 - 16x = 0, which is what we are trying to show. For questions like this, you know that you have arrived at the right answer if you can show that your answer is equivalent to the answer given in the question part - the examiner is simply interested in seeing how it is that you got to the answer (in other words, there are loads of 'working out' marks).
Hi @Sheyda Khan-Mohammadi, nice to see you OnlyPhysics again!
This question initially seems very difficult but it is really just testing whether you break down what it is that the question is asking. We are given two numbers, (x-1), x and (x+1). We are also given that the product of the three numbers is five times their sum.
To work out the product we must simplify: (x-1)(x)(x+1). Essentially, we are expanding three brackets. To do this, just expand the first two brackets as you would normally and simplify. Then, expand this new bracket with the remaining last bracket. I have included an image of how to do this below:
Then, we must work out the sum of the three numbers. So we must do: (x-1) + x + (x+1). This is fairly simple and comes out to 3x. However, we are given that the product of the three numbers is five times their sum. Thus we must multiply 3x by 5 to get 15x.
We can now say that 15x is equal to the product of the three numbers, which is x^3 - x in this case. That is the answer to part a.
For part b, we just have to rearrange the equation x^3 - x = 15x by subtracting 15x from both sides of the equation. We will therefore get x^3 - 16x = 0, which is what we are trying to show. For questions like this, you know that you have arrived at the right answer if you can show that your answer is equivalent to the answer given in the question part - the examiner is simply interested in seeing how it is that you got to the answer (in other words, there are loads of 'working out' marks).
Let us know if you need any more help :)
Thanks a lot for the help!