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NDA 2023 Maths · Mathematics · Application of Derivatives · easy

The sum of two positive numbers is 20. The minimum value of the sum of their squares is

Single correct option

The sum of two positive numbers is 2020. The minimum value of the sum of their squares is
  1. A. 100100
  2. B. 400400
  3. C. 200200
  4. D. 00
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Answer: (C) 200200

Let the numbers be xx and 20−x20-x: S=x2+(20−x)2S=x^2+(20-x)^2. S′=4x−40=0S'=4x-40=0 gives x=10x=10, S′′=4>0S''=4>0, and S=100+100=200S=100+100=200. The value 400400 is SS at the end points x=0x=0 or 2020 (the maximum on the closed range).
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Original question written in the NDA 2023 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake