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AP EAMCET201822 Apr 2018Morning ShiftMathematicsQuadratic EquationActual

For real number x , if the minimum value of f(x)=x^2+2 b x+2 c^2 is greater than the maximum value of g(x)=-x^2-2 c x+b^2 , then

Options

  1. Ac^2>2 b^2
  2. Bc^2 < 2 b^2
  3. Cb^2=2 c^2
  4. Dc^2=2 b^2

Correct answer

A. c^2>2 b^2

Step-by-step solution

We have, aligned f(x) & =x^2+2 b x+2 x^2 & =(x+b)^2+2 x^2-b^2 aligned Minimum value of aligned f(x) & =2 c^2-b^2 g(x) & =-x^2-2 c x+b^2 .x-b^2 ] & =- [(x+c)^2-b^2-c^2 ] & =-(x+c)^2+b^2+c^2 aligned Again, aligned =- [x^2+2 x-b^2 ] & =- [(x+c)^2-b^2-c^2 ] & =-(x+c)^2+b^2+c^2 aligned Maximum value of g(x)=b^2+c^2 Now, according to the question. 2 c^2-b^2>b^2+c^2 c^2>2 b^2

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