Step 1: Find (x² + 1)²
[tex](x^2+1)^2=(x^2)^2+2x^2+1=x^4+2x^2+1[/tex]
Step 2: Find (x² - 1)²
[tex](x^2-1)^2=(x^2)^2-2x^2+1=x^4-2x^2+1[/tex]
Step 3: Find the sum of (x² - 1)² + (2x)²
[tex]\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}[/tex]
Comparing the final result in step 1 with the final result in step 2
[tex](x^2-1)^2+(2x)^2=(x^2+1)^2[/tex]
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
