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Question

If the sum of two distinct positive numbers is 8 and the difference between the arithmetic mean and harmonic mean of the given two numbers is 1, then the value of the largest number is


  1. 4

  2. 6

  3. 7

  4. 8


Solution

The correct option is D

8


Let the two distinct positive numbers be a and b .

a + b = 8

(a+b)22ab(a+b)=1(a+b)24ab=2(a+b)(ab)2=16ab=4

Solving we get a =6 , b= 2

The largest number among the two is 6

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