Find a unit vector x?in R³ at which Q(x) is maximized, subject to x^Tx?= 1. [Hint:?The eigenvalues of the matrix of the quadratic form Q are 2, ?1, and ?4]

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Let Q(x) = -2x − x² + 4x₁x₂ + 4x2x3. Let Q(x) = -2x − x² + 4x₁x₂ + 4x2x3.