## anonymous one year ago Which combination of integers can be used to generate the Pythagorean triple 7,24,25

1. misty1212

HI!!

2. misty1212

the question is a little unclear, but maybe it is this: all triples can be found by taking whole number $$m,n$$ and computing $m^2-n^2, 2mn, m^2+n^2$ is that what you have to find, $$m$$ and ?

3. Elsa213

Welcome to Openstudy! :D

4. misty1212

@Elsa213 thanks dear, welcome to you as well!

5. Elsa213

Thank you cx

6. anonymous

its apex so the answers would be like A.x=4,y=3 B.X=1, y+3 C.x=3,y=2 D.x=2 y=2

7. misty1212

what does "it is apex" mean?

8. anonymous

and thanks for the warm welcome and its an online class

9. misty1212

ok it looks like they used $$x$$ and $$y$$ whereas i used $$m$$ and $$n$$ but it is the same thing

10. anonymous

11. misty1212

you have $x^2-y^2=7$ that is the same as $(x-y)(x+y)=7$ there is only one way to factor $$7$$ as $$1\times 7$$ so $x-y=1\\ x+y=7$ and using that you can solve for $$x$$ and $$y$$

12. anonymous

so i basically plug in and solve

13. misty1212

you can solve that in your head: two numbers that add to 7 and are one apart

14. anonymous

basicaly A

15. misty1212

basically A?

16. anonymous

ooh i see A is $$x=4,y=3$$ yes, that is right