The simplified value of \sqrt{6}+2}/{\\sqrt{2}+\\sqrt{2+\\sqrt{3}}- {\\sqrt{6}-2}/{\\sqrt{2}-\\sqrt{2-\\sqrt{3}}- {2 \\sqrt{2}/{2+\sqrt{2} is

SSC CPO SI and ASI 2015 Paper

Question : 146 of 199

Marks: +1, -0

The simplified value of

{√{6}+2}/{\√{2}+\√{2+\√{3}}}-\ {\√{6}-2}/{\√{2}-\√{2-\√{3}}}- {2 \√{2}}/{2+√{2}}

Solution:

(2)

\ {\√{6}+2}/{\√{2}+√{2+\√{3}}}- {\√{6}-2}/{√{2}-\√{2-\√{3}}}-\ {2 √{2}}/{2+\√{2}}

Multiplying and dividing by √2 in first two terms and rationalising the third term, we get,

=\ {\√{2} ×\√{6}+2 \√{2}}/{\√{2} × √{2}+√{4+2 \√{3}}}-\ {\√{2} ×√{6} -2 \√{2}}/{\√{2} ×√{2} -\√{4-2 \√{3}}}-\ {2 \√{2}}/{2+\√{2}} ×{2-\√{2}}/{2-\√{2}}

= {2 \√{3}+2 \√{2}}/{2+\√{(\√{3}+1)^{2}}}

-\ {2 \√{3}-2 \√{2}}/{2- √{(\√{3}-1)^{2}}}

-2 \√{2}+2

= {2 \√{3}+2 \√{2}}/{3+\√{3}}-\ {2 \√{3}-2 \√{2}}/{3-\√{3}}-2 \√{2}+2

=\ { ( \ {}{6 \√{3}+6 \√{2}-6-2 \√{6}-} \ {6√{3}+6 √{2}-6+2 \√{6}}\ )}/{9-3}-2√ {2}+2

=\ {12 \√{2}-12}/{6}-2 \√{2}+2

=2 \√{2}-2-2 \√{2}+2=0

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