SSC CGL Tier II 1 Dec 2016 Paper 1

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Question : 69 of 100

Marks: +1, -0

If

x= {√{5}+1}/{√{5}-1}

and

y= {√{5}-1}/{√{5}+1}

the value of

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

is

$3 /4$
$4/ 3$
$3 /5$
$5 /3$

Solution:

(2)

x= {√{5}+1}/{√{5}-1}

= {(√{5}+1)^{2}}/{(√{5}-1)(√{5}+1)}

(Rationalising the denominator)

= {5+1+2 √{5}}/{5-1}= {6+2√{5}}/{4}

= {3+√{5}}/{2}

∴

y= {√{5}-1}/{√{5}+1}= {3-√{5}/{2}

∴ x+y= {3+√{5}}/{2}+ {3-√{5}}/{2}

= {3+√{5}+3-√{5}}/{2}=3

x y= {3+√{5}}/{2}×{3-√{5}}/{2}

= {9-5}/{4}=1

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

= {(3)^{2}-1}/{(3)^{2}-3}= {9-1}/{9-3}= {8}/{6}= {4}/{3}

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