<PRE><B>Question 71057</B>
Twice a number equals the difference of 6 and 4 times its reciprocal. What are the possible numbers?
:
x = possible numbers
:
2x = 6 - 4(1/x)
:
Get rid of the denominator, multiply equation by x:
2x^2 = 6x - 4
:
2x^2 - 6x + 4 = 0; our old friend, the quadratic equation
:
Simplify, divide equation by 2 and you have an easily factored equation
x^2 - 3x + 2 = 0
(x-2)(x-1) = 0
x = 2
and
x = 1
:
Check using x = 2
2(2) = 6 - 4(1/2)
4 = 6 - 2
:
Check using x = 1
2 = 6 - 4
:
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