SSC CGL 16 Aug 2015 Shift 2 Paper

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Question : 136 of 200

Marks: +1, -0

If x =

{√5-√3}/{√5+√3}

and y =

{√5+√3}/{√5-√3}

then the value of

{x^2+xy+y^2}/{x^2-xy+y^2}

= ?

${63}/{61}$
${67}/{65}$
${65}/{63}$
${69}/{67}$

Solution:

x =

{√5-√3}/{√5+√3}

, y =

{√5+√3}/{√5-√3}

∴ x + y =

{√5-√3}/{√5+√3}

+

{√5+√3}/{√5-√3}

=

{(√5-√3)^2+(√5+√3)^2}/{(√5+√3)+(√5-√3)}

=

{2((√5)^2+(√3)^2)}/{5-3}

= 5 + 3 = 8
xy =

{√5-√3}/{√5+√3}

×

{√5+√3}/{√5-√3}

= 1
∴

{x^2+xy+y^2}/{x^2-xy+y^2}

=

{(x+y)^2-xy}/{(x+y)^2-3xy}

=

{8^2-1}/{8^2-3}

=

{64-1}/{64-3}

=

{63}/{61}

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