Question

question 8 of 10
which combination of integers can be used to generate the pythagorean
triple (5, 12, 13)?

a. ( x = 1, y = 3 )

b. ( x = 3, y = 2 )

c. ( x = 3, y = 4 )

d. ( x = 2, y = 2 )

Explanation:

Step1: Recall Euclid's formula

Euclid's formula for Pythagorean triples: $a = x^2 - y^2$, $b = 2xy$, $c = x^2 + y^2$ where $x > y > 0$.

Step2: Test option A ($x=1,y=3$)

$x < y$, invalid (needs $x > y$).

Step3: Test option B ($x=3,y=2$)

$a=3^2-2^2=9-4=5$, $b=2×3×2=12$, $c=3^2+2^2=13$. Matches $(5,12,13)$.

Step4: Verify other options (optional)

Option C: $a=9-16=-7$ (invalid). Option D: $a=4-4=0$ (invalid).

Answer:

B. $x = 3,y = 2$