# Deductive Proofs

1. Apr 10, 2006

### Hollysmoke

I don't get any of this and the textbook doesn't help that much either. I was wondering if someone could help me wiht this one question:

Prove that every positive integer, ending in 5 creates a number that when squared, ends in 25.

2. Apr 10, 2006

### matt grime

What did you try? As a hint, what happens if I square 10x for an x?

3. Apr 10, 2006

### Hollysmoke

I didn't try anything because I just don't understand. But I think we have to make it so that a number ending in 5, so 5,15,25, that when squared = ****25

4. Apr 10, 2006

### HallsofIvy

Staff Emeritus
Please don't double post! I'll add what I did to matt grime's post in the other thread. Any integer, ending in 5, can be written in the form 10x+ 5 where x is an integer. What is (10x+ 5)2?

5. Apr 10, 2006

### Hollysmoke

I didn't double post this topic. It may have been someone else with a similar topic.

(10x+5)^2 =100x^+100x+25

And it's 10x+5=*5, which we square, right?

6. Apr 10, 2006

### matt grime

you do not have to 'make it' since it is true, and that is what you're tying to prove.

oh, and you're expansion is slightly off, but surely you can see the answer now, if not express exactly what you need to.

7. Apr 10, 2006

### Hollysmoke

So when I am looking at these types of questions, I should presume that it is true?

8. Apr 10, 2006

### matt grime

Eh? You're asked to prove it is true, so unless there is a mistake somewhere (which is very possible), the answer *is* true, but you cannot assume it is true. But in any case, that has nothing semantically to do with you statement that you want to 'make' it true. *You* do not *make* it true.

9. Apr 10, 2006

### Hollysmoke

Okay I understand. I'm not MAKING it true, I'm just trying to show that it either IS or IS NOT true.

10. Apr 11, 2006

### HallsofIvy

Staff Emeritus
(10x+5)^2 =100x^2+100x+25= 100(x^2+ x)+ 25. What are the last two digits of 100(x^2+ x)? What does that tell you?

(Since you haven't explained what "*" means, I have no idea what you mean by 10x+ 5= *5.)