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

- m²

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-n²

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m²

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Solution

The correct option is A
- m²

If a,b,c is a Pythagorean Triple, then for some natural numbers m and n, where m < n, we have:

a = n² - m², b = 2nm, c = n² + m²

Thus, the value of k is - m²

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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

The correct option is A - m2 If a,b,c is a Pythagorean Triple, then for some natural numbers m and n, where m < n, we have: a = n2 - m2, b = 2nm, c = n2 + m2 Thus, the value of k is - m2

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

The correct option is A
- m²

If a,b,c is a Pythagorean Triple, then for some natural numbers m and n, where m < n, we have:

a = n² - m², b = 2nm, c = n² + m²

Thus, the value of k is - m²