SSC CGL Tier II 25 Oct 2015 Paper 1

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Question : 2 of 100

Marks: +1, -0

Let

x= {√{13}+√{11}}/{√{13}-√{11}}

and

y= {1}/{x}

then the value of

3 x^{2}-5 x y+3 y^{2}

is

1717
1177
1771
1171

Solution:

(1)

x= {√{13}+√{11}}/{√{13}-√{11}}

On rationalising the denominator

= {√{13}+√{11}}/{√{13}-√{11}} ×{√ {13}+ √{11}}/{√{13}+√{11}}

= {(√{13}+√{11})^{2}}/{(√{13})^{2}-(√{11})^{2}}

= {13+11+2 {143}}/{13-11}

= {24+2 √{143}}/{2}=12+√{143}

∴

y= {1}/{x}= {1}/{12+√{143}}

= {1}/{12+√{143}}×{12-√{143}}/{12-√{143}}

= {12-√{143}}/{144-143}=12-√{143}

∴ x-y=12+√{143}-12+ √{143}=2 √{143}

and

x y=(12+√{143})(12-√{143})

=144-143=1

∴ 3 x^{2}-5 x y+3 y^{2}=3 x^{2}-6 x y+ 3 y^{2}+x y

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

=3(2√{143})^{2}+1

=3 × 4 × 143+1=1716+1

=1717

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