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If u= a^2 ^2 +b^2 ^2 + a^2 ^2 +b^2 ^2 , then the difference between the maximum and minimum values of u^2 is given by

Options

  1. A2 (a^2+b^2 )
  2. B2 a^2+b^2
  3. C(a+b)^2
  4. D(a-b)^2

Correct answer

D. (a-b)^2

Step-by-step solution

u= a^2 ^2 +b^2 ^2 + a^2 ^2 +b^2 ^2 = a^2+b^2 2 + a^2-b^2 2 2 + a^2+b^2 2 + b^2-a^2 2 2 u^2=a^2+b^2+2 ( a^2+b^2 2 )^2- ( a^2-b^2 2 )^2 ^2 2 min value of u^2=a^2+b^2+2 a b max value of u^2=2 (a^2+b^2 ) u_ ^2-u_ ^2=(a-b)^2 .

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