Question

In this activity you'll relate polynomial identities to Pythagorean triples.

Answer 1

Step 1: Find (x² + 1)²

`(x^2+1)^2=(x^2)^2+2x^2+1=x^4+2x^2+1`

Step 2: Find (x² - 1)²

`(x^2-1)^2=(x^2)^2-2x^2+1=x^4-2x^2+1`

Step 3: Find the sum of (x² - 1)² + (2x)²

`\begin{gathered} (x^2-1)^2+(2x)^2=x^4-2x^2+1+4x^2=x^4+2x^2+1 \\ (x^2-1)^2+(2x)^2=x^4+2x^2+1 \end{gathered}`

Comparing the final result in step 1 with the final result in step 2

`(x^2-1)^2+(2x)^2=(x^2+1)^2`

Hence, the sum of the squares of the two shorter sides is equal to the square of the longer side

This is a property of right angled triangle

Hence