2023 · Q76
Let α and β be the roots of the equation 1/x = 1/a + 1/b + 1/(x + a + b); a ≠ 0, b ≠ 0, x ≠ 0. Which one of the following is a quadratic equation whose roots are α² and β²?
Elementary MathematicsAlgebra
- Ax² + (a² + b²)x + a²b² = 0
- Bx² − (a² + b²)x + a²b² = 0
- Cx² − (a² + b²)x − a²b² = 0
- Dx² + (a² + b²)x − a²b² = 0
Explanation
As written, 1/x=1/a+1/b+1/(x+a+b) gives x^2-(a^2+4ab+b^2)x+a^2b^2=0, matching no option; option (b) fits 1/(x-a-b), a likely sign slip. Keyed option (b). Key disputed: verify against the official UPSC key.