SOLUTION: If the sum of a rational number and its reciprocal is 13/6,then the number is?

Question 982120: If the sum of a rational number and its reciprocal is 13/6,then the number is?
Found 2 solutions by ikleyn, macston:
Answer by ikleyn(52858)   (Show Source): You can put this solution on YOUR website!

Let x be our rational number.
Then its reciprocal is , and the equation is
+ = .

Multiply both sides by . You will get a quadratic equation

+ = , or

- + = .

Solve it using the quadratic formula. You will get the roots

= and = .

Check:    + = = .

Answer. = and = .

Answer by macston(5194)   (Show Source): You can put this solution on YOUR website!
.
x=number
.

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=0.694444444444459 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 1.50000000000001, 0.666666666666664. Here's your graph:

ANSWER: x=1.5 or x=2/3
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