366/MR00. problem / Math - Solved Math Problems

MR-366 / 366. problem

Solve the following inequality on the set of real numbers!

$x^{2} - x - 2 < 0$

$x^{2} - x - 2 > 0$

a = 1, b = - 1, c = - 2

x_{1, 2} = \frac{- (- 1) \pm \sqrt{{(- 1)}^{2} - 4 \cdot 1 \cdot (- 2)}}{2 \cdot 1}

x_{1, 2} = \frac{1 \pm \sqrt{1 + 8}}{2}

x_{1, 2} = \frac{1 \pm \sqrt{9}}{2}

x_{1, 2} = \frac{1 \pm 3}{2}

x_{1} = \frac{1 + 3}{2}; x_{2} = \frac{1 - 3}{2}

$x_{1} = 2; x_{2} = - 1$

a = 1 \Rightarrow x \in [- 1, 2]

$x \in [- 1, 2]$

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