SSC CHSL 15 Nov 2015 Shift 2 Paper

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Question : 129 of 200

Marks: +1, -0

If

x/y={a+2}/{a-2}

,then the value of

{x^2 −y^2}/{x^2 +y^2}

is :

${2a}/{a^2 +2}$
${4a}/{a^2 +4}$
${2a}/{a^2 +4}$
${4a}/{a^2 +2}$

Solution:

Given :

x/y={a+2}/{a-2}

Squaring both sides, we get :
⇒

x^2/y^2=({a+2})^2/({a-2})^2

Using componendo and dividendo,

{x^2 −y^2}/{x^2 +y^2}={(a+2)^2 −(a−2)^2}/{(a+2)^2 +(a−2)^2}

=

{(a^2 +4a+4)−(a^2 −4a+4)}/{(a^2 +4a+4)+(a^2 −4a+4)}

=

{8a}/{2a^2 +8}

=

{4a}/ {a^2 +4}

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