A) \[3,\frac{1}{3}\]
B) \[3,\frac{-1}{3}\]
C) \[-3,\frac{1}{3}\]
D) \[-3,\frac{-1}{3}\]
Correct Answer: A
Solution :
(a): Let the numbers are x and \[\frac{1}{x}\]. Then, \[x+\frac{1}{x}=\frac{10}{3}\] \[\frac{{{x}^{2}}+1}{x}=\frac{10}{3}\,\,\,\,\Rightarrow 3{{x}^{2}}-10x+3=0\] \[\Rightarrow 3{{x}^{2}}-9x-x+3=0\Rightarrow 3x(x-3)-1(x-3)=0\]\[\Rightarrow \left( 3x-1 \right)\left( x-3 \right)=0\,\,\,\,\therefore x=3,\frac{1}{3}\]
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