SSC CGL 16 Aug 2017 Shift 1 Paper

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Question : 61 of 100

Marks: +1, -0

When

[x+(1 / x)]=5,

then what is the value of

[x-(1 / x)] ?

11
$±√22$
21
$±√21$

Solution:

∵

x+ {1}/{x}=5

⇒

x^{2}+1=5 x

⇒

x^{2}-5 x+1=0

∴

x= {-b +√{b^{2}-4 a c}}/{2 a}

= {-5± √{25-4}}/{2 × 1}=\ {5 ±√{21}}/{2}

So,

x- {1}/{x}= {5+√{21}}/{2}-\ {2}/{5+√{21}}

= {5+√{21}}/{2}- {2(5-√{21})}/{(5+√{21})(5-√{21})}

=\ {5+√{21}}/{2}- {(10-2 √{21})}/{25-21}

= {5+√{21}}/{2}- {(5-√{21})}/{2}

= {5+√{21}-5+√{21}}/{2}

= {2√{21}}/{2}=√{21}

Again,

x- {1}/{x}= {5-√{21}}/{2}- {2}/{5-√{21}}

= {5-√{21}}/{2}- {2}/{5-√{21}}

×{5+√{21}}/{5+√{21}}

= {5-√{21}}/{2}- {10-2 √{21}}/{4}

= {10-2 √{21}-10-2√{21}}/{4}

=- {4 √{21}}/{4}=-√{21}

∴ x- {1}/{x}=\±√{21}

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