Mathematic Problems

260. példa

\sqrt[3]{x} + \sqrt[3]{x + 1} + \sqrt[3]{x + 2} = 0

\sqrt[3]{x} + \sqrt[3]{x + 1} = - \sqrt[3]{x + 2}

{(\sqrt[3]{x} + \sqrt[3]{x + 1})}^{3} = {(- \sqrt[3]{x + 2})}^{3}

{(\sqrt[3]{x})}^{3} + 3 {(\sqrt[3]{x})}^{2} \cdot \sqrt[3]{x + 1} + 3 \sqrt[3]{x} \cdot {(\sqrt[3]{x + 1})}^{2} + {(\sqrt[3]{x + 1})}^{3} = - (x + 2)

x + 3 \sqrt[3]{x} \cdot \sqrt[3]{x + 1} (\sqrt[3]{x} + \sqrt[3]{x + 1}) + x + 1 = - x - 2

\sqrt[3]{x} + \sqrt[3]{x + 1} + \sqrt[3]{x + 2} = 0 \Rightarrow \sqrt[3]{x} + \sqrt[3]{x + 1} = - \sqrt[3]{x + 2}

x + 3 \sqrt[3]{x} \cdot \sqrt[3]{x + 1} \cdot \sqrt[3]{x + 2} (- \sqrt[3]{x + 2}) + x + 1 = - x - 2

- 3 \sqrt[3]{x} \cdot \sqrt[3]{x + 1} \cdot \sqrt[3]{x + 2} = - x - x - x - 2 - 1

- 3 \sqrt[3]{x (x + 1) (x + 2)} = - 3 x - 3

- 3 \sqrt[3]{x (x + 1) (x + 2)} = - 3 (x + 1) / \cdot (- \frac{1}{3})

\sqrt[3]{x (x + 1) (x + 2)} = x + 1

{(\sqrt[3]{x (x + 1) (x + 2)})}^{3} = {(x + 1)}^{3}

x (x + 1) (x + 2) = {(x + 1)}^{3}

x_{1} = - 1 \Rightarrow 0 = 0

x = - 1

x = - 1

Matematika - Képlettár