Question

write a Pythagorean triplet whose greatest number is 257

Answer 1

$We\ know\ that, \\ \\ if\ a^2 + b^2 = c^2, \\ \\ then, \\ \\ a = m^2 - n^2 \\ \\ b = 2mn \\ \\ c = m^2 + n^2$

$257\ can\ be\ written\ as\ m^2 + n^2. \\ \\ 257 = 256 + 1 = 16^2 + 1^2 \\ \\ \therefore m = 16; n = 1 \\ \\ \\ a = m^2 - n^2 = 16^2 - 1^2 = 256 - 1 = 255 \\ \\ b = 2mn = 2 \times 16 \times 1 = 32 \\ \\ \\ 255,\ 32,\ 257\ is\ a\ Pythagorean\ triplet. \\ \\ Here,\ 257\ is\ the\ greatest.$

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Answer 2

Answer:

Step-by-step explanation: