Mathematics - Quadratic Equation Question with Solution | TestHub

MathematicsQuadratic EquationInequationMedium2 minPYQ_2020

MathematicsMediumsingle choice

If $x, y$ and $z$ are real numbers, the $x^{2} + 4 y^{2} + 9 z^{2} - 6 yz - 3 z x - 2 x y$ is always

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Answer:

Solution:

$x^{2} + 4 y^{2} + 9 z^{2} - 6 yz - 3 z x - 2 x y$ $= x^{2} + (2 y)^{2} + (3 z)^{2} - (2 y) (3 z) - (3 z) (x) -$ $x (2 y) \geq 0\forall x, y, z$ $[∵ a^{2} + b^{2} + c^{2} - ab - bc - ca \geq 0]$

Stream:JEESubject:MathematicsTopic:Quadratic EquationSubtopic:Inequation

⏱ 2mℹ️ Source: PYQ_2020

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