If a= {\\sqrt{x+2}+\sqrt{x-2}/{ \sqrt{x+2}-\\sqrt{x-2} , then the value of (a^{2}-a x ) is

SSC CPO SI and ASI 2015 Paper

Question : 115 of 199

Marks: +1, -0

a= {\√{x+2}+√{x-2}}/{ √{x+2}-\√{x-2}}

, then the value of

\ (a^{2}-a x\ )

Solution:

(3) Using componendo and dividendo,

{a+1}/{a-1}

=\ {\√{x+2}+\√{x-2}+\√{x+2}-\√{x-2}}/{\√{x+2}+\√{x-2}-\√{x+2}+\√{x-2}}

= {2 \√{x+2}}/{2 \√{x-2}}

Squaring both sides

\ {a^{2}+2 a+1}/{a^{2}-2 a+1}=\ {x+2}/{x-2}

Using componendo and dividendo again,

\ {2\ (a^{2}+1\ )}/{4 a}=\ {x+2+x-2}/{x+2-x+2}

⇒ \ {\ (a^{2}+1\ )}/{a}=x

a^{2}+1=a x \⇒ a^{2}-a x=-1

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