$$2 + \frac{6}{{\sqrt 3 }} + \frac{1}{{2 + \sqrt 3 }} + \frac{1}{{\sqrt 3 - 2}}$$ equals to
A. +(2√3)
B. -(2 + √3)
C. 1
D. 2
Answer: Option D
Solution(By Examveda Team)
$$\eqalign{ & 2 + \frac{6}{{\sqrt 3 }} + \frac{1}{{2 + \sqrt 3 }} + \frac{1}{{\sqrt 3 - 2}} \cr & \Rightarrow 2 + \frac{{2 \times 3\sqrt 3 }}{{\sqrt 3 \times \sqrt 3 }} + \frac{1}{{2 + \sqrt 3 }} - \frac{1}{{2 - \sqrt 3 }} \cr & \Rightarrow 2 + 2\sqrt 3 + \left( {\frac{{\left( {2 - \sqrt 3 } \right) - \left( {2 + \sqrt 3 } \right)}}{{\left( {2 + \sqrt 3 } \right)\left( {2 - \sqrt 3 } \right)}}} \right) \cr & \Rightarrow 2 + 2\sqrt 3 + \left( {\frac{{2 - \sqrt 3 - 2 - \sqrt 3 }}{{4 - 3}}} \right) \cr & \Rightarrow 2 + 2\sqrt 3 - 2\sqrt 3 \cr & \Rightarrow 2 \cr} $$Related Questions on Surds and Indices
A. $$\frac{1}{2}$$
B. 1
C. 2
D. $$\frac{7}{2}$$
Given that 100.48 = x, 100.70 = y and xz = y2, then the value of z is close to:
A. 1.45
B. 1.88
C. 2.9
D. 3.7
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