| The simplified value of \[(\sqrt{6}+\sqrt{10}-\sqrt{21}-\sqrt{35})\] \[(\sqrt{6}-\sqrt{10}+\sqrt{21}-\sqrt{35})\]is [SSC (CPO) 2014] |
A) 13
B) 12
C) 11
D) 10
Correct Answer: D
Solution :
| \[(\sqrt{6}+\sqrt{10}-\sqrt{21}-\sqrt{35})(\sqrt{6}-\sqrt{10}+\sqrt{21}-\sqrt{36})\]\[=\{(\sqrt{6}-\sqrt{35}+(\sqrt{10}-\sqrt{21})\}\] |
| \[\{(\sqrt{6}-\sqrt{35})-(\sqrt{10}-\sqrt{21})\}\] |
| \[={{(\sqrt{6}-\sqrt{35})}^{2}}-{{(\sqrt{10}-\sqrt{21})}^{2}}=(6+35-2\sqrt{6}\cdot \sqrt{35})\] \[-\,\,(10+21-2\sqrt{10}\cdot \sqrt{21})\] |
| \[=41-2\sqrt{210}-31+2\sqrt{210}=41-31=10\] |
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