Mathematic Problems

245. példa

\sqrt{2 x^{2} - x} = x - 2

\sqrt{2 x^{2} - x} = x - 2 \Rightarrow x - 2 \geq 0 \Rightarrow x \geq 2

{(\sqrt{2 x^{2} - x})}^{2} = {(x - 2)}^{2}

2 x^{2} - x = x - 2

2 x^{2} - x = x^{2} - 4 x + 4

2 x^{2} - x - x^{2} + 4 x - 4 = 0

x^{2} + 3 x - 4 = 0

a = 1, b = 3, c = - 4

x_{1, 2} = \frac{- 3 \pm \sqrt{3^{2} - 4 \cdot 1 \cdot (- 4)}}{2 \cdot 1} = \frac{- 3 \pm \sqrt{9 + 16}}{2} = \frac{- 3 \pm \sqrt{25}}{2} = \frac{- 3 \pm 8}{2}

x_{1} = \frac{- 3 + 5}{2} = \frac{2}{2} x_{2} = \frac{- 3 - 5}{2} = \frac{- 8}{2}

x_{1} = 1 x_{2} = - 4

(x = 1 \lor x = - 4) \land x \geq 2 \Rightarrow x \in \{\emptyset\}

x \in \{\emptyset\}

x \in \{\emptyset\}

Matematika - Képlettár