2019 · Q21
For x = 4√6/(√2 + √3), what is the value of (x + 2√2)/(x - 2√2) + (x + 2√3)/(x - 2√3)?
Elementary MathematicsAlgebra
- A1
- B√2
- C√3
- D2
Explanation
Rationalising, x = 4√6/(√2+√3) = 4√6(√3−√2) = 12√2 − 8√3. Then (x+2√2)/(x−2√2) = (7√2−4√3)/(5√2−4√3) = 11 + 4√6, and (x+2√3)/(x−2√3) = 3(2√2−√3)/(6√2−5√3) = −9 − 4√6. Adding gives exactly 2.