Question

If x+1/x=9 and x²+1/x²=53, Find the value of x-1/x


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Answer 1

Step-by-step explanation:

ANSWER IS SHOWN IN ABOVE IMAGE

Answer 2

Answer:

1) ± 5

Step-by-step explanation:

1) Given:  $x + \frac{1}{x} = 9$ and $x^{2} + \frac{ 1 }{x^{2} } = 53$

    Find: $x - \frac{ 1}{x}$

    $(x + \frac{1}{x})^{2} + (x- \frac{1}{x})^{2} = 2 (x^{2} + \frac{ 1 }{x^{2} } )$

    ( 9² + $(x- \frac{1}{x})^{2}$) = 2 (53)

    $(x- \frac{1}{x})^{2}$ = 106 - 81

                  = 25

     $x - \frac{ 1}{x}$     = ± 5

The question can also be interpreted as:

2) Given: $x + \frac{1}{x} = 9$ and $x^{2} + \frac{ 1 }{x^{2} } = 53$

   Find:  $x - \frac{ 1}{x}$  

   $(x- \frac{1}{x})^{2}$  = x² + $\frac{1}{x^{2} }$ - 2x * $\frac{1}{x^{2} }$                        (a + b)² = a² +b² -2ab)

                     = 53 - 2

                     = 51

   $x - \frac{ 1}{x}$ =  $\sqrt{51}$