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8 June, 00:35

Let a and b be real numbers satisfying a^3 - 3ab^2 = 47 and b^3 - 3a^2 b = 52. Find a^2 + b^2.

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  1. 8 June, 01:24
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    Answer: a²+b² = - 99/2

    Step-by-step explanation:

    Since we are given two equations, this equations will be solved simultaneously to get a² and b²

    a³ - 3ab² = 47 ... 1

    b³ - 3a² b = 52 ... 2

    From 1, a (a² - 3b²) = 47 ... 3

    From 2, b (b² - 3a²) = 52 ... 4

    Adding 3 and 4, we have;

    a²+b²-3b²-3a² = 99 (note that a and b will no longer be part of the equations as they have been factored out)

    a²+b² - (3b²+3a²) = 99

    (a²+b²) - 3 (b²+a²) = 99

    Taking the difference we have

    - 2 (a²+b²) = 99

    a²+b² = - 99/2
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