If $$3\sqrt {\frac{{1 - a}}{a}} + 9 = 19 - 3\sqrt {\frac{a}{{1 - a}}} ,$$ then what is the value of a?
A. $$\frac{3}{{10}},\,\frac{7}{{10}}$$
B. $$\frac{1}{{10}},\,\frac{9}{{10}}$$
C. $$\frac{2}{5},\,\frac{3}{5}$$
D. $$\frac{1}{5},\,\frac{4}{5}$$
Answer: Option B
Solution(By Examveda Team)
$$\eqalign{ & {\text{Put }}\sqrt {\frac{{1 - a}}{a}} = x \cr & \Rightarrow 3x + 9 = 19 - \frac{3}{x} \cr & \Rightarrow 3x + \frac{3}{x} = 10 \cr & \Rightarrow x = 3,\,\frac{1}{3} \cr & {\text{Now, }}\sqrt {\frac{{1 - a}}{a}} = 3 \cr & \Rightarrow \frac{{1 - a}}{a} = 9 \cr & \Rightarrow 10a = 1 \cr & \Rightarrow a = \frac{1}{{10}} \cr & {\text{and }}\sqrt {\frac{{1 - a}}{a}} = \frac{1}{3} \cr & \Rightarrow \frac{{1 - a}}{a} = \frac{1}{9} \cr & \Rightarrow 10a = 9 \cr & \Rightarrow a = \frac{9}{{10}} \cr & \therefore \,a = \frac{1}{{10}}\,{\text{and }}\frac{9}{{10}} \cr} $$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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