A) a = 11, b = 11
B) a = 11, b = 6
C) a = ?11,b = -6
D) a = 11, b = - 6
Correct Answer: D
Solution :
Now, \[\frac{5+2\sqrt{3}}{7+4\sqrt{3}}=\frac{5+2\sqrt{3}}{7+4\sqrt{3}}\times \frac{7-4\sqrt{3}}{7-4\sqrt{3}}\] \[=\frac{35-20\sqrt{3}+14\sqrt{3}-24}{{{\left( 7 \right)}^{2}}-{{\left( 4\sqrt{3} \right)}^{2}}}\] \[=\frac{11-6\sqrt{3}}{49-48}\] \[\Rightarrow \frac{11-6\sqrt{3}}{1}=a+6\sqrt{3}\left( given \right)\] On comparing, we get a = 11 and b = - 6
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