The sum of a number and its reciprocal is ^@\dfrac { 34 } { 15 } | Math Question and Answer | Edugain Russia

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

Answer:

$\dfrac { 3 } { 5 }$ or $\dfrac { 5 } { 3 }$

Step by Step Explanation:

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

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