Question

x+√(x²-1)/x-√(x²-1)+x-√(x²-1)/x+√(x²-1)=14 then what is the value of x?​

Answer 1

SOLUTION

TO DETERMINE

The value of x when

$\displaystyle \sf{ \frac{x + \sqrt{ {x}^{2} - 1 } }{x - \sqrt{ {x}^{2} - 1} } + \frac{x - \sqrt{ {x}^{2} - 1 } }{x + \sqrt{ {x}^{2} - 1} } = 14}$

EVALUATION

Here it is given that

$\displaystyle \sf{ \frac{x + \sqrt{ {x}^{2} - 1 } }{x - \sqrt{ {x}^{2} - 1} } + \frac{x - \sqrt{ {x}^{2} - 1 } }{x + \sqrt{ {x}^{2} - 1} } = 14}$

$\displaystyle \sf{ \implies \: \frac{{(x + \sqrt{ {x}^{2} - 1 } )}^{2} + {(x + \sqrt{ {x}^{2} - 1 } )}^{2} }{(x - \sqrt{ {x}^{2} - 1})(x + \sqrt{ {x}^{2} - 1}) } = 14}$

$\displaystyle \sf{ \implies \: \frac{{2( {x}^{2} + {x}^{2} - 1 } ) }{( {x}^{2} - {x}^{2} + 1)} = 14}$

$\displaystyle \sf{ \implies \: 2(2 {x}^{2} - 1) = 14}$

$\displaystyle \sf{ \implies \: (2 {x}^{2} - 1) = 7}$

$\displaystyle \sf{ \implies \:2 {x}^{2} = 8 }$

$\displaystyle \sf{ \implies \: {x}^{2} = 4 }$

$\displaystyle \sf{ \implies \:x = \pm \: 2}$

FINAL ANSWER

The required value

$\sf{x = \pm \: 2}$

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