Question 1208349
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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
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            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.
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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.



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


But your next equation, 


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(m^2 - n^2)^2 + (2mn)^2 = m^2 + n^2


is written incorrectly.



Its correct version is


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(m^2 - n^2)^2 + (2mn)^2 = (m^2 + n^2)^2.



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<U>Comment from student</U>: 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?



<U>My response</U>:  I just explained to you, where is your next error.



Your next equation, 


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(m^2 - n^2)^2 + (2mn)^2 = m^2 + n^2


is written incorrectly.



Its correct version is


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(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.