The sum of a number and its reciprocal is ^@\dfrac { 34 } { 15 }^@. Find the number.


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Answer:

^@\dfrac { 3 } { 5 }^@ or ^@ \dfrac { 5 } { 3 }^@

Step by Step Explanation:
  1. Let the number is ^@x^@. Then
    ^@ \begin{align} & x + \dfrac {1} {x} = \dfrac { 34 } { 15 } \\ \implies & \dfrac { x^2 + 1 } {x} = \dfrac { 34 } { 15 } \\ \implies & 15x^2 + 15 = 34x \\ \implies & 15x^2 - 34x + 15 = 0 \\ \implies & 15x^2 - 9x - 25x + 15 = 0 \\ \implies & 3x(5x - 3) - 5 (5x - 3) = 0 \\ \implies & (3x - 5) (5x - 3) = 0 \end{align} ^@
  2. Hence, ^@x = \dfrac { 3 } { 5 } \space or \space \dfrac { 5 } { 3 } ^@

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