If x = 2 + √3, y = 2 - √3, z = 1 then what is the value of $$\frac{x}{{yz}} + \frac{y}{{xz}} + \frac{z}{{xy}} + 2\left[ {\frac{1}{x} + \frac{1}{y} + \frac{1}{z}} \right]?$$
A. 25
B. 22
C. 17
D. 43
Answer: Option A
Solution(By Examveda Team)
$$\eqalign{ & x = 2 + \sqrt 3 \cr & y = 2 - \sqrt 3 \cr & z = 1 \cr & \frac{x}{{yz}} + \frac{y}{{xz}} + \frac{z}{{xy}} + 2\left[ {\frac{1}{x} + \frac{1}{y} + \frac{1}{z}} \right] \cr & = \frac{{{x^2} + {y^2} + {z^2}}}{{xyz}} + 2\left[ {\frac{1}{x} + \frac{1}{y} + \frac{1}{z}} \right] \cr & = \frac{{{{\left( {2 + \sqrt 3 } \right)}^2} + {{\left( {2 - \sqrt 3 } \right)}^2} + {{\left( 1 \right)}^2}}}{{\left( {2 + \sqrt 3 } \right)\left( {2 - \sqrt 3 } \right)\left( 1 \right)}} + 2\left[ {\frac{1}{{\left( {2 + \sqrt 3 } \right)}} + \frac{1}{{\left( {2 - \sqrt 3 } \right)}} + 1} \right] \cr & = \frac{{4 + 3 + 4\sqrt 3 + 4 + 3 - 4\sqrt 3 + 1}}{1} + 2\left[ {2 - \sqrt 3 + 2 + \sqrt 3 + 1} \right] \cr & = 15 + 10 \cr & = 25 \cr} $$Related Questions on Algebra
If $$p \times q = p + q + \frac{p}{q}{\text{,}}$$ then the value of 8 × 2 is?
A. 6
B. 10
C. 14
D. 16
A. $$1 + \frac{1}{{x + 4}}$$
B. x + 4
C. $$\frac{1}{x}$$
D. $$\frac{{x + 4}}{x}$$
A. $$\frac{{20}}{{27}}$$
B. $$\frac{{27}}{{20}}$$
C. $$\frac{6}{8}$$
D. $$\frac{8}{6}$$
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