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Rational Expression

Solve the fol...

Question

Solve the following equation:
$\sqrt[3]{16 - x^{3}} = 4 - x$

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Solution

$\sqrt[3]{16 - x^{3}} = 4 - x 16 - x^{3} = {(4 - x)}^{3} 16 - x^{3} = 64 - 48 x + 12 x^{2} - x^{3} 12 x^{2} - 48 x + 48 = 0 x^{2} - 4 x + 4 = 0 {(x - 2)}^{2} = 0 x = 2$

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