Question

Which of the following equations represents a two-variable identity incorporating x and y, where x > 1, x > y, and both x and y are positive integers?

a) (x² - y²)² - (2xy)² = (x² + y²)²

b) (x² + y²)² + (2xy)² = (x² - y²)²

c) (x² - y²)² + (2xy)² = (x² + y²)²

d) (x² - y²)² + (2xy)² = (x² - y²)²

Answer 1

The equation that represents a two-variable identity incorporating x and y, where x > 1, x > y, and both x and y are positive integers, is option c) (x² - y²)² + (2xy)² = (x² + y²)².

Step-by-step explanation:

The equation that represents a two-variable identity incorporating x and y, where x > 1, x > y, and both x and y are positive integers, is option c) (x² - y²)² + (2xy)² = (x² + y²)². To determine this, we can compare the given conditions with the equation in each option. In option c, we have x² - y² ≥ 0, which satisfies the condition x > y, and (x² - y²)² + (2xy)² = (x² + y²)², which satisfies the condition x > 1. Therefore, option c is the correct answer.