Question

The set of integers {3, 4, 5} is a Pythagorean triple. another such set is?

Answer 1

you can multiply each number by any fixed constant if you want another one, say \(\{6,8,10\}\)

Answer 2

but if you want to be more creative and find more that are not multiples of the one you have, there are infinitely many
for example \(\{5,12,13\}\)

Answer 3

okay well this question is multiple choice and the answers I have are 6,7,8
6,8,12
6,12,13
and
8,15,17

Answer 4

in fact if you want say 7 to be one side, you can write
\[m+n=7,m-n=1\implies m=4,n=3\] and then use
\[\{7, 2\times 4\times 3,4^2+3^2\}\] giving the triple
\[\{7,24,25\}\]

Answer 5

in that case, your job is not to find one, but to check if
\[a^2+b^2=c^2\]

Answer 6

for example
\[8^2+15^2=17^2\]
\[64+225=289\] which is true
the others will be false

Answer 7

ohh okay that makes sense so I just have to check it the pythagorean theorem works

Answer 8

yeah, right

Answer 9

so the answer would be the {8,15,17}

Answer 10

yes, obviously.

Answer 11

thanks so much !

Answer 12

i have another question

Answer 13

close this question and post it