Question

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Which set of integers is not a Pythagorean triple?

A.
9, 40, 41

B.
11, 60, 61

C.
15, 18, 21

D.
20, 21, 29

Answer 1

a Pythagorean triple \(a,b,c\) has the property that \(a^2+b^2=c^2\)

The best known triple is probably \(3,4,5\)

Answer 2

A trick you could use to find which ones might work or not without having to square all the numbers:

the last digit of the square is the last digit of the number you are squaring, squared. So 41^2 = some number ending in 1. If we square 9, that ends in 1. If we square 40, that ends in 0. 0+1=1 so the first one might work. If we ended up with something like 1+3, then we would know that was not a triple.

Answer 3

so if \(15,17,19\) was on the list:

last digit of 15^2 = 5*5 = 25 so 5
last digit of 17^2 = 7*7 = 49 so 9
last digit of 19^2 = 9*9 = 81 so 1
5+9 = 14, which doesn't have 1 as its final digit, so we would know that \(15,17,19\) is not a triple.

Answer 4

eliminate A, B, and D
15^2=225
18^2=324
225+324=549
21^2=441
549=441 ( N/A) it doesnt work
So C is your answer

Answer 5

C