Given:
The three equations for the three numbers are
[tex]a=x^2-y^2[/tex]
[tex]b=2xy[/tex]
[tex]c=x^2+y^2[/tex]
To find:
The Pythagorean triple generated by using 4 for x and 1 for y.
Solution:
Substituting x=4 and and y=1 in the given equations, we get
[tex]a=4^2-1^2[/tex]
[tex]a=16-1[/tex]
[tex]a=15[/tex]
In the same way find b and c.
[tex]b=2(4)(1)[/tex]
[tex]b=8[/tex]
The third number is
[tex]c=4^2+1^2[/tex]
[tex]c=16+1[/tex]
[tex]c=17[/tex]
The required Pythagorean triple is 8, 15, and 17.
Therefore, the correct option is C.
