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ludmilkaskok [199]
3 years ago
7

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

Mathematics
1 answer:
KIM [24]3 years ago
5 0

Answer:

D. x=4, y=1

Step-by-step explanation:

We know that,

<em>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.</em>

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.

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