If x=5-2 \sqrt{6}, then what is the value of \\sqrt{x}+(1 / \sqrt{x}) ?

SSC CGL 16 Aug 2017 Shift 1 Paper

Question : 63 of 100

Marks: +1, -0

x=5-2 √{6},

then what is the value of

\√{x}+(1 / √{x})\ ?

Solution:

x=5-2 √{6} ⇒√{x}=√{5-2√{6}}

=√{3}+2-2 √{3}× √{2}

=√{(\√{3}-\√{2})^{2}}=\√{3}-√{2}

and

{1}/{√{x}}= {1}/{√{3}-√{2}}

= {1}/{√{3}-√{2}}× {√{3}+√{2}}/{√{3}+√{2}}

= {\√{3}+\√{2}}/{3-2}=\√{3}+√{2}

∴ √{x}+ {1}/{√{x}}=√{3}-√{2}+√{3}+√{2}

= 2√3

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