Question

Give two more integer solutions of the equation z2 = x2+y2 . Remember that you are only allowed to work with non-zero integers (whole numbers- no fractions, no decimal point numbers

Answer 1

Two additional integer solutions to the equation z^2 = x^2 + y^2 are (3, 4, 5) and (5, 12, 13), which both satisfy the Pythagorean theorem.

Step-by-step explanation:

The equation z2 = x2 + y2 refers to the Pythagorean theorem, which relates the lengths of sides of a right triangle. The question is asking for integer solutions, meaning that all variables x, y, and z must be whole numbers.

Here are two more integer solutions to the equation:

1. x = 3, y = 4, and z = 5. This is a well-known Pythagorean triplet, satisfying 32 + 42 = 52.
2. x = 5, y = 12, and z = 13. This solution also satisfies the equation given by 52 + 122 = 132.

Both of these solutions are sets of positive integers that work with the original equation, providing additional examples alongside the already known (x=2, y=2, z=2) solution.