The sum of a number and its reciprocal is 2 9/10. Find the number.

If you need to answer this, first you need to know the formula...

The "QUADRATIC FORMULA"
For real numbers a, b and c, with a = 0, the solution of the quadratic equation ax^2 + bx + c = 0 is given by the quadratic formula....

x= +
-b _(square root of) b^2 -4ac
_______________________________
2a

To solve this problem, let's assume the number is "x".

According to the problem, the sum of the number and its reciprocal is 2 9/10, or 2.9 as a decimal.
So, we can write the equation as:
x + 1/x = 2.9

To solve this equation, we can multiply both sides by x to clear the fractions:
x^2 + 1 = 2.9x

Now, rearrange the equation to make it a quadratic equation:
x^2 - 2.9x + 1 = 0

To solve this quadratic equation, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)

Applying the formula to our equation, where a = 1, b = -2.9, and c = 1, we can calculate the value(s) of x.

x = (-(-2.9) ± √((-2.9)^2 - 4*1*1))/(2*1)

Simplifying further:

x = (2.9 ± √(8.41 - 4))/2

x = (2.9 ± √4.41)/2

Calculating the square root of 4.41:

x = (2.9 ± 2.1)/2

Now, we have two possible solutions:

1. x = (2.9 + 2.1)/2 = 5/2 = 2.5
2. x = (2.9 - 2.1)/2 = 0.8/2 = 0.4

So, the two possible numbers that satisfy the given condition are 2.5 and 0.4.

Let the number be x.

then
x+1/x=29/10
Solve for x.
The answers are rational fractions.