If a number is subtracted from twice its reciprocal, the result is -23/5. What is the number?

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Answer 1 · 2016-06-19T02:00:32

The number is either 5 or #-2/5#

Let x be the number.

We are told that the number subtracted from twice its reciprocal is equal to #-23/5#

Hence: #2/x - x = -23/5#

Multiply through by x and cross multiply #-> 5(2-x^2) = -23x#

Expand #-> 10-5x^2 = -23x#

#-5x^2+23x+10 = 0#

#5x^2-23x-10 = 0#

Factorise #-> (x-5)(5x+2) = 0#

Hence x = either 5 or #-2/5#