SSC CGL 7 06 2019 Shift 1 Paper

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Question : 71 of 100

Marks: +1, -0

If

\ {6 x}/{2 x^{2}+5 x-2}=1, x>0,

then the value of

x^{3}+\ {1}/{x^{3}}

is:

$3/8√17$
${5√17}/8$
${5√17}/16$
$3/4√17$

Solution:

6 x=2 x^{2}+5 x-2

6=2 x+5-\ {2}/{x}

x-\ {1}/{x}=\ {1}/{2}

Now,

x+\ {1}/{x}=\√{\ {1}/{4}+4}=\√{\ {17}/{4}}

x^{3}+\ {1}/{x^{3}}=a^{3}-3 a

=\ {17}/{4} \√{\ {17}/{4}-3 \√{\ {17}/{4}}}

=\ {17 \√{17}}/{8}-\ {3 \√{17}}/{2}=\ {5 \√{17}}/{8}

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