Question

use polynomial identity list 10 pythagorean triples (x^2+y^2)^2=(x^2-y^2)^2+(2xy)^2

Answer 1

pick to numbers, one even one odd, make them small
we can do this in our heads

Answer 2

lol pick TWO small numbers
like 2 and 3 say

Answer 3

let me know when you pick two

Answer 4

\[\large{(x^2 + y^2)^2 = (x^2 - y^2)^2 + (2xy)^2}\]

What are pythogorean triplets?

Let a, b and c be a set of pythogorean triplet then:

\[\large{c^2 = a^2 + b^2}\]

where: c > a and b

Now, what if I choose:

\[\large{x^2 + y^2 = c}\]
\[\large{x^2 - y^2 = a}\]
\[\large{2xy = b}\]

Answer 5

They satisfy the pythogorean triplet condition.

Now, only thing you need to do is to select some set of values of x and y and evaluate a, b and c which will be your required set of pythogorean triplet

Answer 6

Lets take an example:

x = 2 and y = 1:

\[\large{c = x^2 + y^2 = 2^2 + 1^2 = 4 + 1 = 5}\]
\[\large{a = x^2 - y^2 = 2^2 - 1^2 = 4 - 1 = 3}\]
\[\large{b = 2xy = 2 * 2*1 = 4}\]

So,

(a,b,c) = (3,4,5) is one set of pythogorean triplet

Answer 7

Can you now find another set of pythogorean triplet ? @cabette