Four Absolute Constraints

★ 7/10Absolute ValuealgebrainequalitySymmetry

Problem

Real numbers x,y,zx, y, z satisfy

{∣x+2y−3z∣⩽6,∣x−2y+3z∣⩽6,∣x−2y−3z∣⩽6,∣x+2y+3z∣⩽6.\begin{cases} |x + 2y - 3z| \leqslant 6,\\ |x - 2y + 3z| \leqslant 6,\\ |x - 2y - 3z| \leqslant 6,\\ |x + 2y + 3z| \leqslant 6. \end{cases}

Find the maximum value of ∣x∣+∣y∣+∣z∣|x| + |y| + |z|.

Answer

Solution

Difficulty7/10
TopicsAbsolute Value, algebra, inequality, Symmetry

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