Question : If the sum of two positive numbers is 65 and the square root of their product is 26, then the sum of their reciprocals is:
Option 1: $\frac{7}{52}$
Option 2: $\frac{5}{52}$
Option 3: $\frac{1}{52}$
Option 4: $\frac{3}{52}$
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Correct Answer: $\frac{5}{52}$
Solution :
Let the two numbers be $a$ and $b$.
According to the question,
⇒ $a + b$ = 65 and $\sqrt{ab}$ = 26
So, $ab$ = 26 × 26 = 676
Now, the sum of reciprocals = $\frac{1}{a}$ + $\frac{1}{b}$ = $\frac{b+a}{ab}$ = $\frac{65}{676}$= $\frac{5}{52}$
Hence, the correct answer is $\frac{5}{52}$.
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