Question

3. What three numbers are the Pythagorean triple generated by using 4 for x and 1 for y. Remember to use the formulas:

Answer 1

Given:

The three equations for the three numbers are

$a=x^2-y^2$

$b=2xy$

$c=x^2+y^2$

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

$a=4^2-1^2$

$a=16-1$

$a=15$

In the same way find b and c.

$b=2(4)(1)$

$b=8$

The third number is

$c=4^2+1^2$

$c=16+1$

$c=17$

The required Pythagorean triple is 8, 15, and 17.

Therefore, the correct option is C.