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Let (x + iy)^(1/3) = a + ib. Establish that x/a + y/b = 4(a² - b²).

1. x/a + y/b = 4(a² - b²)
2. x/a + y/b = 2(a² - b²)
3. x/a + y/b = 4(a² + b²)
4. x/a + y/b = a² - b²

Correct answer: x/a + y/b = 4(a² - b²)

Solution

Cubing gives x = a(a² - 3b²) and y = b(3a² - b²); forming x/a + y/b yields 4a² - 4b².

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