SSC CGL 10 Aug 2017 Shift 1 Paper

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Question : 64 of 100

Marks: +1, -0

If

{x+√{x^2-1}}/{x-√{x^2-1}}+{x-√{x^2-1}} /{x+√{x^2-1}}=194,

then what is the value of x ?

$7/2$
4
7
14

Solution:

{x+√{x^2-1}}/{x-√{x^2-1} }+{x-√{x^2-1}} /{x+√{x^2-1}}=194

⇒

{ ({x+√{x^2-1})^2}+({x-√{x^2-1})^2} }/{x^2-(√{x^2-1})^2}

=194

⇒

{x^2 + x^2 - 1 + 2x√{x^2 - 1} + x^2+x^ 2 - 1- 2 x√{x^2 - 1}}/{x^2-x^2+1}=194

⇒

4x^2 -2 =194

⇒

4x^2=196⇒x^2=49

⇒

x=√49

∴ x = 7

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