If $$x = 3 + 2\sqrt 2 ,$$ then the value of $$\left( {\sqrt x - \frac{1}{{\sqrt x }}} \right)$$ is:
A. 1
B. 2
C. $$2\sqrt 2 $$
D. $$3\sqrt 3 $$
Answer: Option B
Solution(By Examveda Team)
$$\eqalign{ & {\left( {\sqrt x - \frac{1}{{\sqrt x }}} \right)^2} \cr & = x + \frac{1}{x} - 2 \cr & = \left( {3 + 2\sqrt 2 } \right) + \frac{1}{{\left( {3 + 2\sqrt 2 } \right)}} - 2 \cr & = \left( {3 + 2\sqrt 2 } \right) + \frac{1}{{\left( {3 + 2\sqrt 2 } \right)}} \times \frac{{\left( {3 - 2\sqrt 2 } \right)}}{{\left( {3 - 2\sqrt 2 } \right)}} - 2 \cr & = \left( {3 + 2\sqrt 2 } \right) + \left( {3 - 2\sqrt 2 } \right) - 2 \cr & = 4 \cr & \therefore \left( {\sqrt x - \frac{1}{{\sqrt x }}} \right) = 2 \cr} $$Join The Discussion
Comments ( 1 )
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
I don't get the fourth line.