| If \[\sqrt{2}=1.4142,\]find the value of \[2\sqrt{2}+\sqrt{2}+\frac{1}{2+\sqrt{2}}-\frac{1}{\sqrt{2}-2}\] [SSC (CGL) 2011] |
A) 1.4144
B) 2.8284
C) 28.284
D) None of these
Correct Answer: D
Solution :
| Expression \[=2\sqrt{2}+\sqrt{2}+\frac{1}{2+\sqrt{2}}-\frac{1}{\sqrt{2}-2}\] |
| \[=3\sqrt{2}+\left( \frac{1}{2+\sqrt{2}}+\frac{1}{2-\sqrt{2}} \right)\] |
| \[=3\sqrt{2}+\left( \frac{2-\sqrt{2}+2+\sqrt{2}}{(2+\sqrt{2})(2-\sqrt{2})} \right)\] |
| \[=3\sqrt{2}+\frac{4}{2}\] |
| \[\Rightarrow \] \[3\sqrt{2}+2=3\times 1.414+2=6.242\] |
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