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Answer:
<h2>65</h2>Step-by-step explanation:
Use PEMDAS:
P Parentheses first
E Exponents (ie Powers and Square Roots, etc.)
MD Multiplication and Division (left-to-right)
AS Addition and Subtraction (left-to-right)
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Assume the first even integer is x.
The next even integer will be 2 digits after this digit. So the next even integer will be x+2.
The reciprocals of these two even integers can be written as
and 
respectively.
The sum of their reciprocals is 7/24. So we can set up the equation as:
Taking LCM on left hand side:
Cross Multiplying the denominators:
Using the quadratic formula to solve the above equation:
Since, the value of x can only be an integer, we discard the fractional value and keep x=6
So the first even integer is 6 and the next even integer is 8. The sum of reciprocals of 6 and 8 is 7/24
The next even integer will be 2 digits after this digit. So the next even integer will be x+2.
The reciprocals of these two even integers can be written as
The sum of their reciprocals is 7/24. So we can set up the equation as:
Taking LCM on left hand side:
Cross Multiplying the denominators:
Using the quadratic formula to solve the above equation:
Since, the value of x can only be an integer, we discard the fractional value and keep x=6
So the first even integer is 6 and the next even integer is 8. The sum of reciprocals of 6 and 8 is 7/24