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Q.

Find the two positive numbers whose sum is 15 and the sum of whose squares is minimum.


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a

  Question Image

b

Question Image

c

Question Image

d

 Question Image 

answer is A.

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Detailed Solution

 Concept- The derivative tests must be used to determine a function's minimum value.
Here, we'll convert two numbers into a function of a certain variable called x.
Say the numbers are x and y whose sum is 15.
Question ImageSay S be the sum of squares of those numbers
Question ImageFrom equation (1) substitute the value of y in the above equation
Question ImageQuestion ImageHence, the correct answer is option 1.
 
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Find the two positive numbers whose sum is 15 and the sum of whose squares is minimum.