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Paragraph: Given that m( )= ^2 +n^2 ^2 +2 n , where n is a fixed positive real number. Question: What is the least value of m ( ) ?

Options

  1. An
  2. B2 n
  3. C3 n
  4. D4 n

Correct answer

D. 4 n

Step-by-step solution

m( )= ^2 +n^2 ^2 +2 n AM GM ^2 +n^2 ^2 2 ^2 n^2 ^2 ^2 +n^2 ^2 2 n For minimum value, ^2 +n^2 ^2 =2 n m( )_ =2 n+2 n=4 n

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