Question

Which identity resulted from the proof in part A, which showed that a triangle with side lengths x2 − 1, 2x, and x2 + 1 is a right triangle?

Answer 1

(x2 − 1)2 + (2x)2 = (x2 + 1)2

Explanation:

for PLATO users this is the right answer

Answer 2

we know that

In a right triangle

Applying the Pythagorean Theorem

`hypotenuse^(2) =leg1^(2) +leg2^(2)`

In this problem

Let

`hypotenuse=x^(2) +1\\leg1=2x\\ leg2=x^(2) -1`

substitute in the formula above

`hypotenuse^(2) =leg1^(2) +leg2^(2)`

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

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

`(x^(4) +2*x^(2)+1) =(x^(4) +2*x^(2)+1)` ------> is ok

that means that is a right triangle