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

RRB RPF RPSF SI and CONS Model Papers 5 with solutions

Question : 82 of 119

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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