X-3-4X-2-6X-24-0-

Question Number 159179 by cortano last updated on 14/Nov/21

X^{3} - 4 X^{2} - 6 X - 24 = 0

Answered by mr W last updated on 14/Nov/21

l e t X = x + \frac{4}{3}

x^{3} + 3 \times \frac{4}{3} x^{2} + 3 \times \frac{16}{9} x + \frac{64}{27} - 4 \times x^{2} - 4 \times 2 x \times \frac{4}{3} - 4 \times \frac{16}{9} - 6 x - 6 \times \frac{4}{3} - 24 = 0

x^{3} - \frac{34 x}{3} - \frac{992}{27} = 0

Δ = \sqrt{- \frac{34^{3}}{9^{3}} + \frac{496^{2}}{27^{2}}} = \frac{2 \sqrt{638}}{3}

\Rightarrow x = \sqrt[3]{\frac{2 \sqrt{638}}{3} + \frac{496}{27}} - \sqrt[3]{\frac{2 \sqrt{638}}{3} - \frac{496}{27}}

\Rightarrow X = \frac{1}{3} (4 + \sqrt[3]{18 \sqrt{638} + 496} - \sqrt[3]{18 \sqrt{638} - 496}) \approx 5.7635

Commented by cortano last updated on 14/Nov/21

w a w a m a z i n g

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