Manipal MET2021MathematicsBasics of Mathematics
If a^2+b^2+c^2=1 , then a b+b c+c a lies in the interval
Options
- A[ 1 2 , 2 ]
- B[-1, 1 2 ]
- C[- 1 2 , 1 ]
- D[-1,1]
Correct answer
C. [- 1 2 , 1 ]
Step-by-step solution
We know, (a+b+c)^2 0 array lr a^2+b^2+c^2+2 a b+2 b c+2 c a 0 1+2(a b+b c+c a) 0 array (a b+b c+c a) -1 2 ...(i) Also, a^2+b^2+c^2=1 aligned & a^2+b^2+c^2-(a b+b c+c a) & = 1 2 [(a-b)^2+(b-c)^2+(c-a)^2 ] 0 & 1-(a b+b c+c a) 0 aligned a b+b c+c a 1 ...(ii) Hence, from Eqs. (i) and (ii), - 1 2 a b+b c+c a 1