Question

(a) How many ordered pairs (x,y) of integers are there such that \sqrt{x^2 + y^2} = 5? Does the question have a geometric interpretation?

(b) How many ordered triples (x,y,z) of integers are there such that \sqrt{x^2 + y^2 + z^2} = 7? Does the question have a geometric interpretation?

By geometric interpretation we mean, "Is there a picture that describes the question?"

Answer 1

@amistre64
@myininaya

Answer 2

@Hero

Answer 3

Well, your choices are rather few, as they must stay in [-5,5]

(-5,0) and (5,0) are pretty obvious.

If you know a little geometry (3,4), (3,-4), (-3,4), (-3,-4) aren't too hard to come by.

The challenge is this, PROVE that there are no more or find any other candidates.

Answer 4

how about 0,5 and 0,-5 and 4,3 and so on? do they count?

Answer 5

this is the equation of a circle, with radius \(5\) centered at the origin.

Answer 6

@tkhunny

Answer 7

Is there more to question. Find that circle and see how many pairs of integers is passes through.

Answer 8

Could you help? I have

Answer 9

@Preetha
@TylerD

Answer 10

@ParthKohli

Answer 11

Try drawing a circle. You'll be done.