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
- A1 2 ; 2
- B-1,2
- C-1, 1 2
- 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