2026 · Q86
For the next two (02) items that follow:
Let x = (√6 + √5)/(√6 − √5) and y = (√6 − √5)/(√6 + √5)
86. What is (x² − xy + y²) equal to?
Elementary MathematicsAlgebra
- A487
- B483
- C481
- D480
Explanation
With x+y=22 and xy=1 from the previous item, x²−xy+y²=(x+y)²−3xy=484−3=481, option C. Equivalently, x²+y²=(x+y)²−2xy=482, so x²−xy+y²=482−1=481. The near-miss options 480 and 483 come from dropping the xy term or mis-adding.