Solve.
-A number minus 20 times its reciprocal is 1. Find the number.
A) 5
B) 5 or 4
C)-5 or 4
D)5 or -4

Question

Quizplus · Accepted Answer

Let the number be x. Then we have the equation x - 20(1/x) = 1. 
Multiplying both sides by x, we get x^2 - 20 = x. 
Bringing all the terms to one side, we get x^2 - x - 20 = 0. 
Factoring this quadratic equation, we get (x-5)(x+4) = 0. 
Therefore, x = 5 or x = -4. 
However, we need to check that the solutions satisfy the original equation. 
For x = -4: -4 - 20(1/-4) = -4 + 5 = 1, which works. 
For x = 5: 5 - 20(1/5) = 1, which also works. 
Thus, the solution is x = 5 or x = -4, and the best choice is D.

Solve. -A Number Minus 20 Times Its Reciprocal Is 1. Find