SOLUTION: Suppose that m and n are opposite integers with m > n. If a = m^2 - n^2, b = 2mn, and c = m^2 + n^2, show that a, b and c are the lengths of the sides of a right triangle. Her

Algebra ->  Triangles -> SOLUTION: Suppose that m and n are opposite integers with m > n. If a = m^2 - n^2, b = 2mn, and c = m^2 + n^2, show that a, b and c are the lengths of the sides of a right triangle. Her      Log On


   

Question 1208349: Suppose that m and n are opposite integers with m > n. If a = m^2 - n^2, b = 2mn, and c = m^2 + n^2, show that a, b and c are the lengths of the sides of a right triangle.

Here is my set up:

a^2 + b^2 = c^2

(m^2 - n^2)^2 + (2mn)^2 = m^2 + n^2
Answer by ikleyn(52798) About Me  (Show Source):
You can put this solution on YOUR website!
.
Suppose that m and n are opposite integers with m > n. If a = m^2 - n^2, b = 2mn, and c = m^2 + n^2, show that a, b and c are the lengths of the sides of a right triangle.

Here is my set up:

a^2 + b^2 = c^2

(m^2 - n^2)^2 + (2mn)^2 = m^2 + n^2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


            This problem is posed INCORRECTLY.


Indeed, if m and n are opposite integers and m > n, it means that m is a positive integer number,
while n is a negative integer number, n = -m.

Then b = 2mn is a negative number.

But negative number can not express the length of the side of a triangle.

This my reasoning proves that the problem formulation in the post is TOTALLY, GLOBALLY and FATALLY defective.


I don't know, from which source did you get this gibberish.


        If to remove the word "opposite" from the condition and replace it by "positive",
        then the problem would be correct and your setup/idea a^2 + b^2 = c^2 would be correct.

But your next equation,

        (m^2 - n^2)^2 + (2mn)^2 = m^2 + n^2

is written incorrectly.


Its correct version is

        (m^2 - n^2)^2 + (2mn)^2 = (m^2 + n^2)^2.


//////////////////////


Comment from student: I made a typo. The correct problem is this one: Suppose that m and n are positive integers with m > n.
If a = m^2 - n^2, b = 2mn, and c = m^2 + n^2, show that a, b and c are the lengths of the sides
of a right triangle. My set up is now correct. True?


My response: I just explained to you, where is your next error.


Your next equation,

        (m^2 - n^2)^2 + (2mn)^2 = m^2 + n^2

is written incorrectly.


Its correct version is

        (m^2 - n^2)^2 + (2mn)^2 = (m^2 + n^2)^2.


..........................................


You see, it's very difficult to discuss your work, since you make mistakes in every line.
You should make your work more responsibly.