The sum of a number and its reciprocal is
29/10 Find the numbers?
You will have two roots (two answers).
Let's assume the number to be x.
According to the given information, the sum of a number and its reciprocal is 29/10.
So, we can set up the equation as:
x + 1/x = 29/10
To solve this equation, we need to eliminate the fraction. Multiplying the entire equation by 10x will help us get rid of the fraction:
10x(x) + 10x(1/x) = (29/10)(10x)
10x^2 + 10 = 29x
Next, bring all terms to one side of the equation:
10x^2 - 29x + 10 = 0
Now, we can factor the quadratic equation or use the quadratic formula to find the values of x. However, this equation does not factor easily, so let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac))/(2a)
In this case, a = 10, b = -29, and c = 10. Substituting these values into the formula:
x = (-(-29) ± √((-29)^2 - 4(10)(10)))/(2(10))
x = (29 ± √(841 - 400))/(20)
x = (29 ± √441)/(20)
x = (29 ± 21)/(20)
Now we have two possible solutions for x:
1. x = (29 + 21)/20 = 50/20 = 5/2
2. x = (29 - 21)/20 = 8/20 = 2/5
Therefore, the two numbers that satisfy the given condition are 5/2 and 2/5.
To find the numbers, let's assume that the first number is x.
According to the problem, the sum of the number and its reciprocal is 29/10.
So, we can write the equation as:
x + 1/x = 29/10
To solve for x, we need to eliminate the fraction by multiplying both sides of the equation by 10x (the common denominator):
10x(x) + 10x(1/x) = 10x(29/10)
Simplifying this equation gives us:
10x^2 + 10 = 29x
Rearranging the terms:
10x^2 - 29x + 10 = 0
Now, we can solve this quadratic equation. We can either factor it or use the quadratic formula. Assuming that factoring is not easily visible, we'll use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Using the quadratic formula, where a = 10, b = -29, and c = 10:
x = (-(-29) ± √((-29)^2 - 4(10)(10))) / (2(10))
Calculating further:
x = (29 ± √(841 - 400)) / 20
x = (29 ± √441) / 20
x = (29 ± 21) / 20
There are two solutions here:
x = (29 + 21) / 20 = 50/20 = 5/2
x = (29 - 21) / 20 = 8/20 = 2/5
Therefore, the two numbers are 5/2 and 2/5.
reciprocal means 1 over the number
x + 1/x = 29/10
solve for x to get your number