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What three numbers are the Pythagorean triple generated by using [tex]$x = 4$[/tex] and [tex]$y = 1$[/tex]? Remember to use the formulas:

[tex]\[a = x^2 - y^2,\][/tex]
[tex]\[b = 2xy,\][/tex]
[tex]\[c = x^2 + y^2.\][/tex]

A. 6, 8, and 10
B. 5, 11, and 12
C. 3, 5, and 8
D. 8, 15, and 17



Answer :

GinnyAnswer
To generate a Pythagorean triple using the formulas [tex]\(a = x^2 - y^2\)[/tex], [tex]\(b = 2xy\)[/tex], and [tex]\(c = x^2 + y^2\)[/tex] with [tex]\(x = 4\)[/tex] and [tex]\(y = 1\)[/tex], let's go through each step in detail.

1. Calculate [tex]\(a\)[/tex]:
[tex]\[ a = x^2 - y^2 \][/tex]
Substitute [tex]\(x = 4\)[/tex] and [tex]\(y = 1\)[/tex]:
[tex]\[ a = 4^2 - 1^2 = 16 - 1 = 15 \][/tex]

2. Calculate [tex]\(b\)[/tex]:
[tex]\[ b = 2xy \][/tex]
Substitute [tex]\(x = 4\)[/tex] and [tex]\(y = 1\)[/tex]:
[tex]\[ b = 2 \cdot 4 \cdot 1 = 2 \cdot 4 = 8 \][/tex]

3. Calculate [tex]\(c\)[/tex]:
[tex]\[ c = x^2 + y^2 \][/tex]
Substitute [tex]\(x = 4\)[/tex] and [tex]\(y = 1\)[/tex]:
[tex]\[ c = 4^2 + 1^2 = 16 + 1 = 17 \][/tex]

Therefore, the Pythagorean triple generated by using [tex]\(x = 4\)[/tex] and [tex]\(y = 1\)[/tex] is [tex]\(a = 15\)[/tex], [tex]\(b = 8\)[/tex], and [tex]\(c = 17\)[/tex].

From the given options, the correct Pythagorean triple is:
[tex]\[ \boxed{8, 15, 17} \][/tex]

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