A) 195
B) 200
C) 175
D) 185
Correct Answer: A
Solution :
[a] Given \[a=\frac{2+\sqrt{3}}{2-\sqrt{3}}\]and \[b=\frac{2-\sqrt{3}}{2+\sqrt{3}}\] \[\therefore \] \[{{a}^{2}}+{{b}^{2}}+ab={{(a+b)}^{2}}-ab\] \[=\left( \frac{2+\sqrt{3}}{2-\sqrt{2}}-\frac{2-\sqrt{3}}{2+\sqrt{3}} \right)\] \[={{\left[ \frac{2\,(4+3)}{4-3} \right]}^{2}}-1\] \[={{(14)}^{2}}-1=195\] |
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