A) \[\frac{1}{4},\ \frac{4}{1}\]
B) \[\frac{3}{4},\ \frac{4}{3}\]
C) \[\frac{2}{5},\ \frac{5}{2}\]
D) \[\frac{3}{2},\ \frac{2}{3}\]
Correct Answer: D
Solution :
Suppose that required numbers \[a\] and\[b\]. Therefore according to the conditions \[a=\frac{1}{b}\] and \[\frac{a+b}{2}=\frac{13}{12}\]\[\Rightarrow \]\[a+b=\frac{13}{6}\] \[\Rightarrow \] \[a+\frac{1}{a}=\frac{13}{6}\Rightarrow 6{{a}^{2}}-13a+6=0\] \[\Rightarrow \] \[\left( a-\frac{3}{2} \right)\,\left( a-\frac{2}{3} \right)=0\]\[\Rightarrow \]\[a=\frac{3}{2}\] and \[b=\frac{2}{3}\] or \[a=\frac{2}{3}\] and \[b=\frac{3}{2}\]. Trick: Find the A.M. of option (a), (b), (c), (d) one by one.
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