Find the simplified value of {1}/{\\sqrt{2}+\\sqrt{3}-\sqrt{5}+ {1}/{\\sqrt{2}-\\sqrt{3}-\\sqrt{5}

SSC CPO SI and ASI 2015 Paper

Question : 137 of 199

Marks: +1, -0

Find the simplified value of

\ {1}/{\√{2}+\√{3}-√{5}}+\ {1}/{\√{2}-\√{3}-\√{5}}

Solution:

(3)

\ {1}/{\√{2}+\√{3}-\√{5}}+\ {1}/{\√{2}-\√{3}-\√{5}}

=\ {\√{2}-\√{3}-\√{5}+√{2}+\√{3}-\√{5}}/{(\√{2}+\√{3}-\√{5})(\√{2}-\√{3}-\√{5})}

= {2(\√{2}-\√{5})}/{(\√{2}-\√{5})^{2}-(\√{3})^{2}}

=\ {2(\√{2}-√{5})}/{2+5-2 \√{10}-3}=\ {\√{2}-\√{5}}/{2-√{10}}

=\ {(\√{2}-√{5})}/{\√{2}(\√{2}-\√{5})}=\ {1}/{√{2}}

Go to Question:

Prev Question

Next Question