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What three numbers are the Pythagorean triple generated by using 4 for [tex]$x$[/tex] and 3 for [tex]$y$[/tex]?

Remember to use the formulas: [tex]$a = x^2 - y^2$[/tex], [tex][tex]$b = 2xy$[/tex][/tex], and [tex]$c = x^2 + y^2$[/tex].

A. 8, 24, and 31
B. 1, 7, and 12
C. 7, 24, and 25
D. 3, 4, and 5

Sagot :

GinnyAnswer
To determine the Pythagorean triple generated by using [tex]\( x = 4 \)[/tex] and [tex]\( y = 3 \)[/tex], we can use the following formulas:

[tex]\[ a = x^2 - y^2 \][/tex]
[tex]\[ b = 2 \cdot x \cdot y \][/tex]
[tex]\[ c = x^2 + y^2 \][/tex]

Let's substitute [tex]\( x \)[/tex] and [tex]\( y \)[/tex] with 4 and 3 respectively into these formulas.

1. Calculate [tex]\( a \)[/tex]:
[tex]\[ a = x^2 - y^2 \][/tex]
[tex]\[ a = 4^2 - 3^2 \][/tex]
[tex]\[ a = 16 - 9 \][/tex]
[tex]\[ a = 7 \][/tex]

2. Calculate [tex]\( b \)[/tex]:
[tex]\[ b = 2 \cdot x \cdot y \][/tex]
[tex]\[ b = 2 \cdot 4 \cdot 3 \][/tex]
[tex]\[ b = 2 \cdot 12 \][/tex]
[tex]\[ b = 24 \][/tex]

3. Calculate [tex]\( c \)[/tex]:
[tex]\[ c = x^2 + y^2 \][/tex]
[tex]\[ c = 4^2 + 3^2 \][/tex]
[tex]\[ c = 16 + 9 \][/tex]
[tex]\[ c = 25 \][/tex]

The three numbers forming the Pythagorean triple are:

[tex]\[ (7, 24, 25) \][/tex]

Therefore, the correct answer from the given options is:

[tex]\[ 7, 24, and 25 \][/tex]
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