2019 · Q9
If [(1 + px)/(1 - px)]√[(1 - qx)/(1 + qx)] = 1, then what are the non-zero solutions of x?
Elementary MathematicsAlgebra
- A±(1/p)√((2p - q)/q), 2p ≠ q
- B±(1/(pq))√(p - q), p ≠ q
- C±(p/p)√(p - q), p ≠ q
- D±(q/p)√(2p - q), 2p ≠ q
Explanation
Squaring gives (1+px)^2(1−qx) = (1−px)^2(1+qx). Expanding and cancelling equal terms leaves 4px − 2qx − 2p^2qx^3 = 0, i.e. 2x(2p − q − p^2qx^2) = 0. For non-zero x, x^2 = (2p−q)/(p^2q), so x = ±(1/p)√((2p−q)/q) with 2p ≠ q.