# Minimum of sum

Find a positive number that the sum of the number and its inverted value was minimal.

Result

x =  1

#### Solution:

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

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!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

## Next similar math problems:

1. Z9–I–1
In all nine fields of given shape to be filled natural numbers so that: • each of the numbers 2, 4, 6 and 8 is used at least once, • four of the inner square boxes containing the products of the numbers of adjacent cells of the outer square, • in the cir
2. Endless lego set
The endless lego set contains only 6, 9, 20 kilograms blocks that can no longer be polished or broken. The workers took them to the gym and immediately started building different buildings. And of course, they wrote down how much the building weighed. They
3. Camp
In a class are 26 children. During the holidays 16 children were in the camps and 14 children on holiday with their parents. Determine the minimum and maximum number of children that may have been in the camp and on holiday with their parents at the same
4. Digits
Write the smallest and largest 1-digit number.
5. Florist's
The florist got 72 white and 90 red roses. How many bouquets can bind from all these roses when each bouquets should have the same number of white and red roses?
6. Three numbers
Create from digits 1-9 three-digit numbers with their sum the smallest. What value is the sum of these numbers? (Use each digit only once)
7. Sphere and cone
Within the sphere of radius G = 33 cm inscribe cone with largest volume. What is that volume and what are the dimensions of the cone?
8. Cone
Into rotating cone with dimensions r = 8 cm and h = 8 cm incribe cylinder with maximum volume so that the cylinder axis is perpendicular to the axis of the cone. Determine the dimensions of the cylinder.
9. Fixed expenses 2013
Since 2013, the Slovak government plans to tax more small one person businesses. Instead of fixed expences 40% will be fixed expences 40% of gross income up to 420 Eur. Calculate what percentage of fixed expences will in 2013 pays from gross income 1569 E
10. Sphere in cone
A sphere of radius 3 cm desribe cone with minimum volume. Determine cone dimensions.
11. Statue
On the pedestal high 4 m is statue 2.7 m high. At what distance from the statue must observer stand to see it in maximum viewing angle? Distance from the eye of the observer from the ground is 1.7 m.