SOLUTION: A number exceeds four times its reciprocal by 3. Find the number.

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Question 530882: A number exceeds four times its reciprocal by 3. Find the number.
Found 2 solutions by oberobic, MathTherapy:
Answer by oberobic(2304)   (Show Source): You can put this solution on YOUR website!
x = a number
.
It exceeds it's reciprocal by 3
.
x = 1/x + 3
.
multiply both sides by x to eliminate the fraction
.
x^2 = 1 + 3x
.
x^2 -3x -1 = 0
.
This will not factor, but it can be solved by the quadratic equation.
.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=13 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 3.30277563773199, -0.302775637731995. Here's your graph:
Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!
A number exceeds four times its reciprocal by 3. Find the number.

Let the number be N

Based on the given info., we can say that:

------ Multiplying by LCD, N



(N - 4)(N + 1) = 0

N, or number = or

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