AP EAMCET · Maths · Quadratic Equation
If \(a^2+b^2+c^2=1, a, b, c \in R\), then the set of extreme values of \(a b+b c+c a\) is
- A \(\left\{\frac{1}{2} ; 2\right\}\)
- B \(\{-1,2\}\)
- C \(\left\{-1, \frac{1}{2}\right\}\)
- D \(\left\{\frac{-1}{2}, 1\right\}\)
Answer & Solution
Correct Answer
(D) \(\left\{\frac{-1}{2}, 1\right\}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & (a-b)^2+(b-c)^2+(c-a)^2 \geq 0 \\ \Rightarrow \quad & 2\left(a^2+b^2+c^2\right)-2(a b+b c+c a) \geq 0 \\ \Rightarrow \quad & a^2+b^2+c^2 \geq a b+b c+c a \\ \Rightarrow \quad & \quad 1 \geq a b+b c+c a \\ \text { Also } & (a+b+c)^2 \geq 0 \\ \Rightarrow &…
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