SOLUTION: Find a number such that subtracting its reciprocal from the number gives 16/15

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Question 1113525: Find a number such that subtracting its reciprocal from the number gives 16/15
Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
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x - 1%2Fx = 16%2F15


15x^2 - 16x - 15 = 0


x%5B1%2C2%5D = %2816+%2B-+sqrt%2816%5E2+%2B+4%2A15%2A15%29%29%2F%282%2A15%29 = %2816+%2B-+34%29%2F30


x%5B1%5D = %2816+%2B+34%29%2F30 = 50%2F30 = 5%2F3


x%5B2%5D = %2816+-+34%29%2F30 = -18%2F30 = -3%2F5



Check.  5%2F3+-+3%2F5 = 25%2F15+-+9%2F15 = 16%2F15.  ! Correct !


        -3%2F5+%2B+5%2F3 = -9%2F15+%2B+25%2F15 = 16%2F15.   ! Correct !


Answer.  Two solutions  are  -3%2F5  and  5%2F3.






Plot y = x+-+1%2Fx (red) and y = 16%2F15 (green)