Question

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Answer 1

$a {x}^{ \frac{2}{3 } } + b {x}^{ \frac{1}{3} } + c = 0 \\ \\ a {x}^{ \frac{2}{3 } } + b {x}^{ \frac{1}{3} } = - c \\ \\ cubing \\ \\ (a {x}^{ \frac{2}{3 } } + b {x}^{ \frac{1}{3} }) ^{3} = - {c}^{3} \\ \\ {a}^{3} {x}^{2} + {b}^{3} x + 3abx(a {x}^{ \frac{2}{3 } } + b {x}^{ \frac{1}{3} }) = - {c}^{3} \\ \\ {a}^{3} {x}^{2} + {b}^{3} x + {c}^{3} = - 3abx(a {x}^{ \frac{2}{3 } } + b {x}^{ \frac{1}{3} }) \\ \\ {a}^{3} {x}^{2} + {b}^{3} x + {c}^{3} = - 3abx( - c) \\ \\ {a}^{3} {x}^{2} + {b}^{3} x + {c}^{3} = 3abcx$

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