Answer:
D. x=4, y=1
Step-by-step explanation:
We know that,
The Pythagorean triples are generated by x, y and [tex](2xy,x^2-y^2,x^2+y^2)[/tex], where x,y > 0 and are integers.
To generate the triple (8,15,17), we have the system,
[tex]2xy=8[/tex] ...........(1)
[tex]x^2-y^2=15[/tex] ............(2)
[tex]x^2+y^2=17[/tex] ............(3)
Adding (2) and (3), we get,
[tex]2x^2=32[/tex]
i.e. [tex]x^2=16[/tex]
i.e. [tex]x=\pm 4[/tex]
Substitute the value of x in (1), we get,
[tex]2\times 4y=8[/tex]
i.e. [tex]8y=8[/tex]
i.e. [tex]y=\pm 1[/tex]
So, we get the integers,
x = 4, y= 1 and x= -4, y= 1.
Thus, according to the options, the integers which generate the triples are x = 4, y= 1.
