Mathematic Problems

197. példa

\frac{x^{3} + 216}{x^{3}} = 36 - x^{3}

\frac{x^{3} + 216}{x^{3}} = 36 - x^{3}

\frac{x^{3} + 216}{x^{3}} = 36 - x^{3} | \cdot x^{3}

\frac{x^{3} + 216}{x^{3}} \cdot x^{3} = 36 \cdot x^{3} - x^{3} \cdot x^{3}

x^{3} + 216 = 36 x^{3} - x^{6}

x^{6} + x^{3} - 36 x^{3} + 216 = 0

x^{6} - 35 x^{3} + 216 = 0

x^{3} = t \Rightarrow x^{6} - 35 x^{3} + 216 = 0 \Rightarrow t^{2} - 35 t + 16 = 0

t^{2} - 35 t + 216 = 0

t^{2} - 35 t + 216 = 0 \Rightarrow a = 1; b = - 35; c = 216

t_{1, 2} = \frac{35 \pm \sqrt{35^{2} - 4 \cdot 1 \cdot 216}}{2 \cdot 1}

t_{1, 2} = \frac{35 \pm \sqrt{1225 - 864}}{2} = \frac{35 \pm \sqrt{361}}{2} = \frac{35 \pm 19}{2}

t_{1} = \frac{35 + 19}{2} = \frac{54}{2} = 27

t_{2} = \frac{35 - 19}{2} = \frac{16}{2} = 8

t_{1} = 27; t_{2} = 8

x_{1}^{3} = t_{1} \Rightarrow x_{1}^{3} = 27 \Rightarrow x_{1} = \sqrt[3]{27} = 3

x_{2}^{3} = t_{2} \Rightarrow x_{2}^{3} = 8 \Rightarrow x_{2} = \sqrt[3]{8} = 2

x_{1} = 3; x_{2} = 2

Helyettesítse az

x^{3}

kifejezést t-vel.

Helyettesítse az

x^{3}

kifejezést t-vel.

Zamenite izraz

x^{3}

sa t.

x_{1} = 3; x_{2} = 2

Matematika - Képlettár