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Question

The sum of two non–zero numbers is 4.

The minimum value of the sum of their reciprocals is


A

34

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B

65

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C

1

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D

None of these.

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Solution

The correct option is C

1


Explanation of the correct option:

Step 1. Find the function

Let two non-zero numbers are x and y.

Given : The sum of two non–zero numbers is 4.

x+y=4

y=4-x

Thus sum of the reciprocals is,

1x+1yx+yxy4x(4-x)

Let f(x)=44x-x2

Step 2. Find the minimum value

f(x)=44x-x2

For extremum f'x=0

f'(x)=-4(4-2x)(4x-x2)2-4(4-2x)(4x-x2)2=04-2x=0x=2

y=2

Therefore, minimum of 1x+1y=12+12

minimum of 1x+1y=1

Hence, option (C) is the correct option.


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