Question

Find all Pythagorean triples with 3 sides in in arithmetic progression?

Answer 1

I know what a Pythagorean triple is, but what do you mean by one having three sides?

Answer 2

Right triangle with Pythagorean triple is a Pythagorean triangle

Answer 3

Think of it as a bit of a hint....

Answer 4

3,4,5
the basic thing!! let me think about the rest

Answer 5

Ofcourse by 3,4,5 I also mean all such triplets..6,8,10 ; 9,12,15 etc

Answer 6

I think there are no more except the 3-4-5 forms

Answer 7

Thinking is good, a proof would be better...:-)

Answer 8

Hint?

Answer 9

(a+d)^2 = a^2 + (a-d)^2
Solving,
4d = a
Putting different values of d, we get different values of a..which are all multiples of 4.
a-d are respective multiples of 3
a+d are respective multples of 5

Answer 10

That will do....

Answer 11

:-)

Answer 12

x^2 + (x+d)^2 = (x+2d)^2 ->

x^2 -2xd -3d^2 = 0 ->

(x-3d)(x+d) = 0 etc.....