SOLUTION: which combination of integers can be used to generate the pythagorean triple? (5,12,13) a. x=3, y=4 b. x=1, y=3 c. x=3, y=2 d. x=2, y=2 please explain dont just write the a

Algebra ->  Trigonometry-basics -> SOLUTION: which combination of integers can be used to generate the pythagorean triple? (5,12,13) a. x=3, y=4 b. x=1, y=3 c. x=3, y=2 d. x=2, y=2 please explain dont just write the a      Log On


   

Question 1026519: which combination of integers can be used to generate the pythagorean triple? (5,12,13)
a. x=3, y=4
b. x=1, y=3
c. x=3, y=2
d. x=2, y=2
please explain dont just write the answer thanks!
Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!
The Pythagorean triples are generated by x,y and

(x²-y²,2xy,x²+y²) where x > y > 0, x,y both integers.

To generate (5,12,13), we have the over-determined system:

system%28x%5E2-y%5E2=5%2C2xy=12%2Cx%5E2%2By%5E2=13%29

Adding the first and third equations:

2x%5E2=18

x%5E2=9

x=3

Substituting x² = 9

x%5E2%2By%5E2=13

9%2By%5E2=13

y%5E2=4

y=2

And if we check we find that x=3, y=2 
satisfies all three equations of the
over-determined system above.

Answer: c

Edwin