we know that
In a right triangle
Applying the Pythagorean Theorem
[tex]hypotenuse^{2} =leg1^{2} +leg2^{2}[/tex]
In this problem
Let
[tex]hypotenuse=x^{2} +1\\leg1=2x\\ leg2=x^{2} -1[/tex]
substitute in the formula above
[tex]hypotenuse^{2} =leg1^{2} +leg2^{2}[/tex]
[tex](x^{2} +1)^{2} =(2x)^{2} +(x^{2} -1)^{2}[/tex]
[tex](x^{4} +2*x^{2}+1) =(4*x^{2})+(x^{4} -2*x^{2}+1)[/tex]
[tex](x^{4} +2*x^{2}+1) =(x^{4} +2*x^{2}+1)[/tex] ------> is ok
that means that is a right triangle
