SOLUTION: when a number is added to 40 times its reciprocal the answer obtained is 2 less than three the number,what is number could be

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Question 703247: when a number is added to 40 times its reciprocal the answer obtained is 2 less than three the number,what is number could be

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
When a number is added to 40 times its reciprocal, the answer obtained is 2 less than three times the number.
What is then number?
:
Let x = the number
write an equation for exactly what it says:
x + 40%2Fx = 3x - 2
x - 3x + 40%2Fx + 2 = 0
-2x + 40%2Fx + 2 = 0
multiply by -x, resulting in an quadratic equation, easily factored:
2x^2 - 2x - 40 = 0
Factors to
(x + 4)(2x - 10) = 0
The positive solution
2x = 10
x = 5 is the number
:
:
See if that works:
5 + 40%2F5 = 3(5) - 2
5 + 8 = 15 - 2
:
:
But what about x = -4
-4 + 40%2F4 = 3(-4) - 2
-4 - 10 = -12 - 2; That works too?