The sum of a number and 20 times its reciprocal is 9. Find the number(s).
Please show working
x + 20/x = 9
x^2 - 9x + 20 = 0
I assume you can take it from here?
is it x=-5 or -4 ??
no,
(x-5)(x-4) = 0
x = 4 or 5
negative numbers have negative reciprocals, so they'd add to -20
I mean add to -9
To solve this problem, let's assume the number is represented by the variable "x".
According to the given information, the sum of a number and 20 times its reciprocal is 9. Mathematically, this can be written as:
x + (20 * (1/x)) = 9
To simplify the equation, we can multiply both sides by "x" to get rid of the fraction:
x * x + 20 = 9x
This simplifies to:
x^2 + 20 = 9x
Now, rearrange the equation to have all the terms on one side:
x^2 -9x + 20 = 0
At this point, we can factorize the equation:
(x - 5)(x - 4) = 0
This gives us two possible solutions for "x":
1) x - 5 = 0 --> x = 5
2) x - 4 = 0 --> x = 4
Thus, the possible values for the number are 5 and 4.