If a non-zero number N, diminished by 4 times its reciprocal, equals a given real constant R, then in terms of R, the sum of all such possible values of N is:
- 1/R
- R
- 4
- 1/4
- –R
Since N – | 4 | = R → N – | 4 | – R = 0 → N2 − 4 − RN = 0 → N2 − RN − 4 = 0. |
N | N |
So we have a nice quadratic in N, and
N = | R ± √R2 + 16 | . |
2 |
So
N = | R + √ | or | N = | R− √ | . |
2 | 2 |
The sum of the N‘s is
R + √ | + | R − √ | = | R | + | √ | + | R | − | √ | = | 2R | = R. |
2 | 2 | 2 | 2 | 2 | 2 | 2 |
The answer is (b).