2017 · Q23
The non-zero solution of the equation (a-x²)/bx - (b-x)/c = (c-x)/b - (b-x²)/cx, where b≠0,c≠0 is
Elementary MathematicsAlgebra
- A(b²+ac)/(b²+c²)
- B(b²-ac)/(b²-c²)
- C(b²-ac)/(b²+c²)
- D(b²+ac)/(b²-c²)
Explanation
Bring the terms together: (a−x²)/bx+(b−x²)/cx = (b−x)/c+(c−x)/b. The left side is [ac+b²−x²(b+c)]/(bcx) and the right side is [b²+c²−x(b+c)]/(bc). Multiplying by bcx gives ac+b²−x²(b+c) = x(b²+c²)−x²(b+c), so x(b²+c²) = ac+b². Hence x = (b²+ac)/(b²+c²), option (A).