Question

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

A. x=2 y=2
B. x=3 y=2
C. x=4 y=3
D. x=4 y=1

Answer 1

D. x=4, y=1

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* 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.