| If \[x-\sqrt{3}-\sqrt{2}=0\] and \[y-\sqrt{3}+\sqrt{2}=0,\]then value of \[({{x}^{3}}-20\sqrt{2})-({{y}^{3}}+2\sqrt{2})\] is |
A) 1
B) 3
C) 0
D) 2
Correct Answer: C
Solution :
| \[x=\sqrt{3}+\sqrt{2}\] and \[y=\sqrt{3}-\sqrt{2}\] |
| \[\therefore \]\[({{x}^{3}}-20\sqrt{2})-({{y}^{3}}+2\sqrt{2})\] |
| \[=[{{(\sqrt{3}+\sqrt{2})}^{3}}-20\sqrt{2}]-[{{(\sqrt{3}-\sqrt{2})}^{3}}+2\sqrt{2}]\] |
| \[=(3\sqrt{3}+2\sqrt{2}+9\sqrt{2}+6\sqrt{3}-20\sqrt{2})-\] |
| \[(3\sqrt{3}-2\sqrt{2}-9\sqrt{2}+6\sqrt{3}+2\sqrt{2})\] |
| \[=(9\sqrt{3}-9\sqrt{2})-(9\sqrt{3}-9\sqrt{2})=0\] |
You need to login to perform this action.
You will be redirected in
3 sec
