Use the polynomial identity below to you create a list of 10 pythagorean triples:
(x²+y²)² = (x²-y²)² + (2xy)²
hint #1: c² = a² + b²
hint #2: pick 2 positive integers x and y, where x > y

(3,4,5)

(6,8,10)

(5,12,13)

(8,15,17)

(12,16,20)

(7,24,25)

(10,24,26)

(20,21,29)

(16,30,34)

(9,40,41)

Just choose 2 numbers from {1,2,3,4,5,6,7,8,...} and make sure the one you input for x is larger.

Post the three in the comments and I will check them for you.

Step-by-step explanation:

We need to choose 2 positive integers for x and y where x>y.

Positive integers are {1,2,3,4,5,6,7,.....}.

I'm going to start with (x,y)=(2,1).

x=2 and y=1.

So one Pythagorean Triple is (3,4,5).

I'm going to choose (x,y)=(3,1).

x=3 and y=1.

So another Pythagorean Triple is (6,8,10).

I'm going to choose (x,y)=(3,2).

x=3 and y=2.

So another is (5,12,13).

I'm going to choose (x,y)=(4,1).

Another is (8,15,17).

I'm going to choose (x,y)=(4,2).

We have another which is (12,16,20).

I'm going to choose (x,y)=(4,3).

We have another is (7,24,25).

You are just choosing numbers from the positive integer set {1,2,3,4,... } and making sure the number you plug in for x is higher than the number for y.

I will do one more.

Let's choose (x,y)=(5,1).

So (10,24,26) is another.

Let (x,y)=(5,2).

So another Pythagorean Triple is (20,21,29).

Choose (x,y)=(5,3).

Another Pythagorean Triple is (16,30,34).

Let (x,y)=(5,4)

Another is (9,40,41).

sorry, i can't understand your question. will later if you describe more clearly!

: )

step-by-step explanation: