Answer:
x=3 and y=2
Step-by-step explanation:
The pythagorean triples are generated by two integrers x and y that can be found by solving the following system of equations:
[tex]\left \{ {{x^{2}-y^{2}=5}\atop {2xy=12}} \atop {x^{2}+y^{2}=13}}\right.[/tex]
Solve the system of equations, and we get that the solution is x=3 and y=2.
Therefore, the combination of integrers that ca be used to generate the pythagorea triple are: x=3 and y=2
Answer:
[tex]x=3[/tex] and [tex]y=2[/tex]
Step-by-step explanation:
The Pythagorean triples can be generated by two values x, y, and a given system of equations:
[tex]x^{2}-y^{2}=5\\2xy=12\\x^{2}+y^{2}=13[/tex]
You can see that each coordinate of the triple is included in each equation.
Remember that Pythagorean triples refers to the values of each side of a right triangle, where is used the Pythagorean Theorem. But, at a higher level, to construct this triples we use the system of equations, with two integers x and y., like this case.
Now we solve the system, the best first step is to just sum the first and third equations, because they have like terms:
[tex]2x^{2}=18\\x^{2}=\frac{18}{2}=9\\x=3[/tex]
Now, we just replace it in the second equation:
[tex]2xy=12\\y=\frac{12}{2x}=\frac{6}{3}=2[/tex]
Therefore the integers that generate the Pythagorean triple [tex](5,12,13)[/tex] are [tex]x=3[/tex] and [tex]y=2[/tex]
