For the next two (02) items that follow:
Let x = (√6 + √5)/(√6 - √5) and y = (√6 - √5)/(√6 + √5)

What is (x² - xy + y²) equal to?

Question

For the next two (02) items that follow:
Let x = (√6 + √5)/(√6 - √5) and y = (√6 - √5)/(√6 + √5)

What is (x² - xy + y²) equal to?

Accepted Answer

481. From the previous, x = 11 + 2√30, y = 11 - 2√30. Then xy = (11)² - (2√30)² = 121 - 120 = 1. Also x + y = 22, so x² + y² = (x + y)² - 2xy = 484 - 2 = 482. Therefore x² - xy + y² = 482 - 1 = 481.

For the next two (02) items that follow: Let x = (√6 + √5)/(√6 - √5) and y = (√6 - √5)/(√6 + √5) What is (x² - xy + y²) equal to?

Explanation

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