Math Problem Statement

Как, при помощи неравенства треугольника ∣a+b∣≤∣a∣+∣b∣\left|a+b\right|\le\left|a\right|+\left|b\right| доказать обратное неравенство треугольника ∣a±b∣≥∣∣a∣−∣b∣∣\left|a\pm b\right|\ge\left|\left|a\right|-\left|b\right|\right|?

Solution

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Math Problem Analysis

Mathematical Concepts

Inequalities
Absolute Value
Triangle Inequality
Linear Algebra

Formulas

Triangle Inequality: $$ \left|a + b\right| \leq \left|a\right| + \left|b\right| $$
Reverse Triangle Inequality: $$ \left|a \pm b\right| \geq \left|\left|a\right| - \left|b\right|\right| $$

Theorems

Triangle Inequality Theorem
Reverse Triangle Inequality Theorem

Suitable Grade Level

Undergraduate level (University)

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