Question

What combination of integers can be used to generate the pythagorean triple (8,15,17)

Answer 1

Answer:

D. x=4, y=1

Step-by-step explanation:

We know that,

The Pythagorean triples are generated by x, y and $(2xy,x^2-y^2,x^2+y^2)$, where x,y > 0 and are integers.

To generate the triple (8,15,17), we have the system,

$2xy=8$            ...........(1)

$x^2-y^2=15$    ............(2)

$x^2+y^2=17$    ............(3)

Adding (2) and (3), we get,

$2x^2=32$

i.e. $x^2=16$

i.e. $x=\pm 4$

Substitute the value of x in (1), we get,

$2\times 4y=8$

i.e. $8y=8$

i.e. $y=\pm 1$

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.