| Which one of the following is true? [SSC (10+2) 2014] |
A) \[\sqrt{5}+\sqrt{3}>\sqrt{6}+\sqrt{2}\]
B) \[\sqrt{5}+\sqrt{3}<\sqrt{6}+\sqrt{2}\]
C) \[\sqrt{5}+\sqrt{3}=\sqrt{6}+\sqrt{2}\]
D) \[(\sqrt{5}+\sqrt{3})=(\sqrt{6}+\sqrt{2})=1\]
Correct Answer: A
Solution :
| \[{{(\sqrt{5}+\sqrt{3})}^{2}}=5+3+2\sqrt{15}=8+2\sqrt{15}\] |
| and \[{{(\sqrt{6}+\sqrt{2})}^{2}}=6+2+2\sqrt{12}=8+2\sqrt{12}\] |
| Again, \[8+2\sqrt{15}>8+2\sqrt{12}\] |
| \[\therefore \] \[\sqrt{5}+\sqrt{3}>\sqrt{6}+\sqrt{2}\] |
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