Simplify : $$\left( {\frac{{\frac{3}{{2 + \sqrt 3 }} - \frac{2}{{2 - \sqrt 3 }}}}{{2 - 5\sqrt 3 }}} \right) = ?$$
A. $$\frac{1}{2} - 5\sqrt 3 $$
B. 2 - $$5\sqrt 3 $$
C. 1
D. 0
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & \frac{{\frac{3}{{2 + \sqrt 3 }} - \frac{2}{{2 - \sqrt 3 }}}}{{2 - 5\sqrt 3 }} \cr & = \frac{{\frac{{3\left( {2 - \sqrt 3 } \right) - 2\left( {2 + \sqrt 3 } \right)}}{{\left( {2 + \sqrt 3 \,} \right)\left( {2 - \sqrt 3 } \right)}}}}{{2 - 5\sqrt 3 }} \cr & = \frac{{6 - 3\sqrt 3 - 4 - 2\sqrt 3 }}{{\left( {2 + \sqrt 3 } \right)\left( {2 - \sqrt 3 } \right)\left( {2 - 5\sqrt 3 } \right)}} \cr & = \frac{{2 - 5\sqrt 3 }}{{2 - 5\sqrt 3 }} \cr & = 1 \cr} $$This Question Belongs to Arithmetic Ability >> Surds And Indices
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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