[JEE Advanced 1984] if a 2 b 2 c 2 1 then ab bc ca lies in
If $a^2+b^2+c^2=1$, then $ab+bc+ca$ lies in the interval
(a) $\left(\frac12,2\right)$
(b) $[-1,2)$
(c) $\left[-\frac12,1\right]$
(d) $\left[-1,\frac12\right]$
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 2d ago
▲ 0
Correct answer: (c) $\left[-\frac12,1\right]$
$(a+b+c)^2\ge0\Rightarrow ab+bc+ca\ge-\frac12$, and $ab+bc+ca\le a^2+b^2+c^2=1$. So it lies in $[-\frac12,1]$.
JEE Advanced 1984 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.
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