Answer:
The set of integers which form a Pythagorean triple is:
5,12,13
Step-by-step explanation:
We are asked to find the set of integers such that they form a Pythagorean triplets.
Three integers a,b,c are said to form a Pythagorean triplets if they satisfy the property:
[tex]c^2=a^2+b^2[/tex]
1)
3,5,6
[tex]6^2=36[/tex]
and
[tex]3^2+5^2=9+25\\=34\neq 36[/tex]
Hence option: 1 is incorrect.
2)
5, 12, 13
[tex]13^2=169[/tex]
and
[tex]5^2+12^2=25+144=169[/tex]
This means:
[tex]13^2=5^2+12^2[/tex]
Hence, option 2 is correct.
3)
15,9,17
[tex]17^2=289[/tex]
Also,
[tex]15^2+9^2=225+81=306\neq 289[/tex]
Hence, option 3 is incorrect.
4)
6,8,12
[tex]12^2=144[/tex]
and:
[tex]6^2+8^2=36+64=100\neq 144[/tex]
Hence, option 4 is incorrect.
