SOLUTION: The difference between a number and its reciprocal is 55/24. Find then number? I did up to this: 24x(x - 1/x = 55/24)24x 24x^2 - 24 = 55x Then???

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Question 987947: The difference between a number and its reciprocal is 55/24. Find then number?
I did up to this:
24x(x - 1/x = 55/24)24x
24x^2 - 24 = 55x
Then???
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
Maybe you felt stuck too quickly.
x, the number
1/x, its reciprocal

x-1%2Fx=55%2F24
24x%28x-1%2Fx%29=%2855%2F24%2924x
24x%5E2-24=55x
highlight_green%2824x%5E2-55x-24=0%29-----Maybe this is factorable and maybe not.

Formula for general solution of quadratic equation:
Discriminant, D=%28-55%29%5E2-4%2A24%2A%28-24%29
D=55%5E2%2B4%2A24%5E2
D=5329
highlight_green%28D=73%5E2%29=5329
-
highlight_green%28highlight_green%28x=%2855%2B-+73%29%2F%282%2A24%29%29%29

highlight%28x=-3%2F4%29 OR highlight%28x=16%2F3%29