2026 · Q85
For the next two (02) items that follow:
Let x = (√6 + √5)/(√6 − √5) and y = (√6 − √5)/(√6 + √5)
85. What is (x² − y²) equal to?
Elementary MathematicsAlgebra
- A22√30
- B44√30
- C66√30
- D88√30
Explanation
Rationalising, x=(11+2√30) and y=(11−2√30) (note xy=1). Then x²−y²=(x−y)(x+y)=(4√30)(22)=88√30, option D. Equivalently, (x−y)(x+y) with x−y=4√30 and x+y=22 gives the product directly.