A) \[\frac{1}{3}(56\sqrt{10}+12)\]
B) \[\frac{1}{3}(56\sqrt{10}-12)\]
C) \[\frac{1}{3}(56+12\sqrt{10})\]
D) None of these
Correct Answer: A
Solution :
Given that,\[y=\frac{\sqrt{5}-\sqrt{2}}{\sqrt{5}+\sqrt{2}}\] and \[x=\frac{\sqrt{5}+\sqrt{2}}{\sqrt{5}-\sqrt{2}}\] \[\Rightarrow \] \[y=\frac{1}{x}\] \[\Rightarrow \] \[xy=1\] \[\therefore \] \[3{{x}^{2}}+4xy-3{{y}^{2}}=3(x-y)\] \[(x+y)+4xy\] \[=3\left( \frac{\sqrt{5}+\sqrt{2}}{\sqrt{5}-\sqrt{2}}-\frac{\sqrt{5}-\sqrt{2}}{\sqrt{5}+\sqrt{2}} \right)\] \[\times \left( \frac{\sqrt{5}+\sqrt{2}}{\sqrt{5}-\sqrt{2}}+\frac{\sqrt{5}-\sqrt{2}}{\sqrt{5}+\sqrt{2}} \right)+4\] \[=3\left[ \frac{{{(\sqrt{5}+\sqrt{2})}^{2}}-{{(\sqrt{5}-\sqrt{2})}^{2}}}{(5-2)(5-2)} \right]\] \[[{{(\sqrt{5}+\sqrt{2})}^{2}}+{{(\sqrt{5}\,-\sqrt{2})}^{2}}]+4\] \[=\frac{1}{3}\cdot 4\sqrt{10}\cdot 2(5+2)+4\] \[=\frac{56}{3}\sqrt{10}+4\] \[=\frac{1}{3}(56\sqrt{10}+12)\]
You need to login to perform this action.
You will be redirected in
3 sec
