If the sum of the squares of a and b is the same as the square of c and if m < n, then for what value of k can the Pythagorean triples be generated with the following equations? a = n2 + k , b = 2mn : c = (m2 + n2 1-:(a) - m2 2-:m2 3-:(-n2) 4-:m

Asked by rejaulhassan | 16th Aug, 2012, 11:16: PM

Expert Answer:

Given that, the sum of the squares of a and b is the same as the square of c.
So, a2 + b2 = c2
(n2 + k)2 + (2mn)2 = (m2 + n2)2
n4 + k2 + 2n2k + 4m2n2 = m4 + n4 + 2m2n2
k2 - m4 + 2n2k + 2m2n2 = 0
 
Clearly, the above relation is satisfied when k = -m2

Answered by  | 17th Aug, 2012, 10:12: AM

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