Question

Argue that a triangle with sides x squared - 1; 2x; x
squared + 1 is a right triangle.? PLEASE i need help.

Answer 1

umm which is the hypoteneuse

Answer 2

it doesn't say

Answer 3

well i think you use the pythagorean theorem.

Answer 4

and ending result you would get 2x

Answer 5

i think

Answer 6

Use the converse of the Pythagorean Theorem. We do not know that the triangle is right; therefore, it has no hypotenuse yet.

The square of one side of the triangle must be equal to the sum of the squares of the other two if the triangle is right.

Square the 3 side lengths to determine if two of the squares sum to the third.

Answer 7

ok thanks directrix ill try that.

Answer 8

Find (x^2 -1) ^2, then (2x)^2, and then (x^2 +1)^2. See what you get. I will check.

Answer 9

Should 2x be x^2 or perhaps (2x^2)^2? Just asking.

Answer 10

:)

Answer 11

no its 2x.

Answer 12

Okay. What did you get for these three quantities?

Find (x^2 -1) ^2, then (2x)^2, and then (x^2 +1)^2.

Answer 13

x^4-1 and 4x^2 and x^4+1

Answer 14

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

Next Step: Will any two of these sum to the third.

Note: Do not exponentiate over addition or subtraction.
( x + y) ^2 is NOT = x^2 + y^2. but does equal x^2 +2xy + y^2.
You are thinking of (xy)^2 which DOES equal x^2 y^2