Find the Pythagorean Triples using the values, $m = 2$ and $n = 3$ .

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Solution

When $m$ and $n$ are any two positive integers $(m < n)$ , then
$a = n^{2} - m^{2}$
$b = 2 n m$
$c = n^{2} + m^{2}$
Then $a, b$ and $c$ are Pythagorean triples
Here $m = 2$ and $n = 3$
$∴ a = 3^{2} - 2^{2}$
$\Rightarrow 9 - 4 = 5$
$∴ b = 2 \times 3 \times 2 \Rightarrow 12$
$∴ c = 3^{2} + 2^{2}$
$\Rightarrow 9 + 4 = 13$
Hence $5, 12, 13$ are Pythagorean triples.

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Find the Pythagorean Triples using the values, m=2 and n=3.

When m and n are any two positive integers (m<n), thena=n2−m2b=2nmc=n2+m2Then a,b and c are Pythagorean triples Here m=2 and n=3∴a=32−22⇒9−4=5∴b=2×3×2⇒12∴c=32+22⇒9+4=13Hence 5,12,13 are Pythagorean triples.

Find the Pythagorean Triples using the values, $m = 2$ and $n = 3$ .