72. Найдите все значения а, при которых равенство верно.

Решение:

Необходимо решить каждое уравнение относительно \( |a| \) и затем найти значения \( a \).

• \( |a| - 10,3 = 20 \) \(\|a\| = 20 + 10,3 \) \(\|a\| = 30,3 \) \( a = \pm 30,3 \)
• \( 5,2 - |a| = 2 \) \(\|a\| = 5,2 - 2 \) \(\|a\| = 3,2 \) \( a = \pm 3,2 \)
• \( |a| = \frac{3}{4} \) \( a = \pm \frac{3}{4} \)
• \( 7|a| = 2,8 \) \(\|a\| = \frac{2,8}{7} \) \(\|a\| = 0,4 \) \( a = \pm 0,4 \)
• \( 12 : |a| = \frac{7}{4} \) \(\|a\| = 12 : \frac{7}{4} = 12 \cdot \frac{4}{7} = \frac{48}{7} \) \( a = \pm \frac{48}{7} \)
• \( 3 + |a| = 6 \) \(\|a\| = 6 - 3 \) \(\|a\| = 3 \) \( a = \pm 3 \)
• \( 5 - 2|a| = -7 \) \(-2|a| = -7 - 5 \) \(-2|a| = -12 \) \(\|a\| = 6 \) \( a = \pm 6 \)
• \( |a + 8| = 2 \) \( a + 8 = 2 \) или \( a + 8 = -2 \) \( a = 2 - 8 = -6 \) или \( a = -2 - 8 = -10 \)
• \( |a| = 4 \) \( a = \pm 4 \)
• \( |a - 2| = 0 \) \( a - 2 = 0 \) \( a = 2 \)
• \( |a + 4| = 2 \) \( a + 4 = 2 \) или \( a + 4 = -2 \) \( a = 2 - 4 = -2 \) или \( a = -2 - 4 = -6 \)
• \( 8 : |a| = 2 \) \(\|a\| = \frac{8}{2} \) \(\|a\| = 4 \) \( a = \pm 4 \)
• \( \frac{1}{2}|a| = 12 \) \(\|a\| = 12 \cdot 2 \) \(\|a\| = 24 \) \( a = \pm 24 \)
• \( \frac{20}{|a|} = 4 \) \(\|a\| = \frac{20}{4} \) \(\|a\| = 5 \) \( a = \pm 5 \)
• \( 3|a| + 2 = 5 \) \(3|a| = 5 - 2 \) \(3|a| = 3 \) \(\|a\| = 1 \) \( a = \pm 1 \)
• \( |a| : \frac{3}{4} = 16 \) \(\|a\| = 16 \cdot \frac{3}{4} \) \(\|a\| = 4 \cdot 3 \) \(\|a\| = 12 \) \( a = \pm 12 \)
• \( |3 - a| = 3 \) \( 3 - a = 3 \) или \( 3 - a = -3 \) \( a = 3 - 3 = 0 \) или \( a = 3 - (-3) = 6 \)

Ответ: \( \pm 30,3 \); \( \pm 3,2 \); \( \pm \frac{3}{4} \); \( \pm 0,4 \); \( \pm \frac{48}{7} \); \( \pm 3 \); \( \pm 6 \); \( -6; -10 \); \( \pm 4 \); \( 2 \); \( -2; -6 \); \( \pm 4 \); \( \pm 24 \); \( \pm 5 \); \( \pm 1 \); \( \pm 12 \); \( 0; 6 \).