[JEE Advanced 1980] if x y z are real and distinct and u x 2 4y 2
If $x,y,z$ are real and distinct and $u=x^2+4y^2+9z^2-6yz-3xz-2xy$, then $u$ is always
(a) non-negative
(b) zero
(c) non-positive
(d) none of these
1 Answer
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✓ Vidaara Team
✓ Accepted
· 2d ago
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Correct answer: (a) non-negative
$u=\tfrac12\big[(x-2y)^2+(2y-3z)^2+(3z-x)^2\big]\ge0$, so $u$ is always non-negative.
JEE Advanced 1980 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.
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