(1)Prove that for every a, b ? R, |a + b| = |a| + |b| ?? ab ? 0.Hint: Write |a + b| 2 = (|a| + |b|) 2 and expand.
(2) Prove that for every x, y, z ? R, |x ? z| = |x ? y| + |y ?z| ?? (x ? y ? z or z ? y ? x). Hint: Use part (1) to prove part(2).
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