CDS 2016 PYQ with Answer — The solution of the inequation 1+1/x-1/x² ≥ 0 is (given that x ≠ 0)

2016 · Q37

The solution of the inequation 1+1/x-1/x² ≥ 0 is (given that x ≠ 0)

Elementary MathematicsAlgebra

Ax > 0
Bx < 0
C(−1−√(5))/2 ≤ x ≤ (−1+√(5))/2
Dx ≤ (−1−√(5))/2 or x ≥ (−1+√(5))/2

Explanation

Multiplying by x² > 0 gives x²+x−1 ≥ 0, whose roots are (−1±√5)/2. The quadratic opens upward, so the inequality holds for x ≤ (−1−√5)/2 or x ≥ (−1+√5)/2, option D. Option C's closed interval between the roots is where the expression is negative (e.g. x = 0.1 gives −89).