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) About Me  (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 ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-3x%2B-1+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-3%29%5E2-4%2A1%2A-1=13.

Discriminant d=13 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--3%2B-sqrt%28+13+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-3%29%2Bsqrt%28+13+%29%29%2F2%5C1+=+3.30277563773199
x%5B2%5D+=+%28-%28-3%29-sqrt%28+13+%29%29%2F2%5C1+=+-0.302775637731995

Quadratic expression 1x%5E2%2B-3x%2B-1 can be factored:
1x%5E2%2B-3x%2B-1+=+1%28x-3.30277563773199%29%2A%28x--0.302775637731995%29
Again, the answer is: 3.30277563773199, -0.302775637731995. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-3%2Ax%2B-1+%29

Answer by MathTherapy(10551) About Me  (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: N+=+4%281%2FN%29+%2B+3

N%5E2+=+4+%2B+3N ------ Multiplying by LCD, N

N%5E2+-+3N+-+4+=+0

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

N, or number = highlight_green%284%29 or highlight_green%28-+1%29

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