# The product

The product of a number plus that number and its inverse is two and one-half. What is the inverse of this number

Correct result:

z =  0.5

#### Solution:

$x + 1/x=2.5 \ \\ \ \\ x^2 + 1=2.5*x \ \\ \ \\ x^2 + 1=2.5 \cdot \ x \ \\ x^2 -2.5x +1=0 \ \\ \ \\ a=1; b=-2.5; c=1 \ \\ D=b^2 - 4ac=2.5^2 - 4\cdot 1 \cdot 1=2.25 \ \\ D>0 \ \\ \ \\ x_{1,2}=\dfrac{ -b \pm \sqrt{ D } }{ 2a }=\dfrac{ 2.5 \pm \sqrt{ 2.25 } }{ 2 } \ \\ x_{1,2}=1.25 \pm 0.75 \ \\ x_{1}=2 \ \\ x_{2}=0.5 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (x -2) (x -0.5)=0 \ \\ \ \\ z=1/x_{1}=1/2=\dfrac{ 1 }{ 2 }=0.5$

Checkout calculation with our calculator of quadratic equations.

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

Tips to related online calculators
Looking for help with calculating roots of a quadratic equation?
Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?

## Next similar math problems:

• Product
The product of two consecutive odd numbers is 8463. What are this numbers?
• Equation with abs value
How many solutions has the equation ? in the real numbers?
• Roots
Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
• Reciprocal equation 2
Solve this equation: x + 5/x - 6 = 4/11
• Fraction
For what x expression ? equals zero?
• Square root 2
If the square root of 3m2 +22 and -x = 0, and x=7, what is m?
55%+36%+88%+71%+100=63% what is whole (X)? Percents can be added directly together if they are taken from the same whole, which means they have the same base amount. .. . You would add the two percentages to find the total amount.
• Solve 3
Solve quadratic equation: (6n+1) (4n-1) = 3n2
Find the roots of the quadratic equation: 3x2-4x + (-4) = 0.
• Equation
Equation ? has one root x1 = 8. Determine the coefficient b and the second root x2.
• Discriminant
Determine the discriminant of the equation: ?
• Water reservoir
The cuboid reservoir contains 1900 hectoliters of water and the water height is 2.5 m. Determine the dimensions of the bottom where one dimension is 3.2 m longer than the second one.
• Birthdays
In the classroom, students always give candy to their classmates on their birthdays. The birthday person always gives each one candy, and he does not give himself. A total of 650 candies were distributed in the class per year. How many students are in the