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Question

If the difference between a number and twice its reciprocal is 24/5, find the number.  ( HINT: use quadratic formula to solve, ANSWER MAY NOT BE A WHOLE VALUE )

Answer 1

x = the number

The wording of the problem translates into

x - 2/x = 24/5

Multiply through by x and get

x² - 2 = (24/5)x

x² - (24/5)x - 2 = 0

Now solve this last equation using the quadratic formula and finish from here.