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AP EAMCET20227 Jul 2022Evening ShiftMathematicsQuadratic EquationActual

If a^2+b^2+c^2=1, a, b, c R , then the set of extreme values of a b+b c+c a is

Options

  1. A1 2 ; 2
  2. B-1,2
  3. C-1, 1 2
  4. D-1 2 , 1

Correct answer

D. -1 2 , 1

Step-by-step solution

aligned & (a-b)^2+(b-c)^2+(c-a)^2 0 & 2 (a^2+b^2+c^2 )-2(a b+b c+c a) 0 & a^2+b^2+c^2 a b+b c+c a & 1 a b+b c+c a Also & (a+b+c)^2 0 & a^2+b^2+c^2+2(a b+b c+c a) 0 & a b+b c+c a - 1 2 & - 1 2 a b+b c+c a 1 aligned

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