According to the book it should be proven this way.
How do you know that you're supposed to do it that way? I know how to get there when I know what they expect from me but if I don't have the solutions I do different operations.
According to the book it should be proven this way.
How do you know that you're supposed to do it that way? I know how to get there when I know what they expect from me but if I don't have the solutions I do different operations.
Any advice would be appreciated. One thing you could do is start with what you are trying to prove and get to a statement you know is true. The sequence of logic written on the paper is an example of this. What is useful is that you can reverse the logic and you then have a proof.
One thing you could do is start with what you are trying to prove and get to a statement you know is true. The sequence of logic written on the paper is an example of this. What is useful is that you can reverse the logic and you then have a proof.
Does (a-b)^2 >= 0 prove the statement? Or are the square roots in the brackets necessary in order to prove the statement?
That's a method called direct proof. There's no contradiction, nor a possibility to list all possible cases.
So in this case, it's a given fact that (a+b)2≥0, and you're working back from that.
It says you use things established to be true, so you can't use the statement you're being asked to prove. In that example, they don't work backwards from the statement, they use known facts - like how integers before and after n are n + 1 and n - 1. That doesn't need proof, that's just a given.