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
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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.