SOLUTION: The sum of a number and its reciprocal is 5/2. What is the number and reciprocal?

Question 102444: The sum of a number and its reciprocal is 5/2. What is the number and reciprocal?
Found 2 solutions by stanbon, Fombitz:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Let the number be "x
EQUATION:
x + 1/x =5/2
Multiply thru by 2x to get:
2x^2+2 = 5x
2x^2-5x+2 = 0
2x^2-4x-x+2=0
2x(x-2)-(x-2)=0
(x-2)(2x-1)=0
x = 2 or x = 1/2
=============
Cheers,
Stan H.

Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!

Multiply both sides by X.
Additive inverse of
Quadratic equation.
We can solve this equation using the quadratic formula where the solution for
is solved by

In this case ,,
Substitute into the quadratic formula.
Multiply both sides by 2, just for convenience.
Subtract fractions in the square root, need same denominator.
Simplify.

Two solutions are
1.
1.
1.
and
2.
2.
2.
Check your answers

True, good answer.

True, good answer.
RELATED QUESTIONS
the sum of a number and four times its reciprocal is -5. what is the... (answered by sofiyacherni,bucky)
The sum of a number and twice its reciprocal is 51/5. What is the number? (answered by greenestamps)
The sum of the reciprocal of 5 and the reciprocal of 7 is the reciprocal of what... (answered by nerdybill)
The sum of the number and twice its reciprocal is 51/5. What is the... (answered by josgarithmetic)
The sum of a number and its reciprocal is 25/12. What is the... (answered by Earlsdon)
the sum of a number and its reciprocal is 10/3 what is the... (answered by cowess,Earlsdon)
The sum of a number and its reciprocal is 10/3. What is the... (answered by stanbon)
the sum of a number and its reciprocal is 10/3. What is the... (answered by checkley77)
The sum of a number and its reciprocal is 10/3. What is the... (answered by josmiceli)