162/MR00. zadatak / Matematika - Zbirka rešenih zadataka

MR-162. zadatak

Rešiti sledeću jednačinu:

$25 x^{2} + 20 \sqrt{3} + 61 = 0$

$25 x^{2} + 20 \sqrt{3} + 61 = 0$

x_{1, 2} = \frac{- 20 \sqrt{3} \pm \sqrt{{(20 \sqrt{3})}^{2} - 4 \cdot 25 \cdot 61}}{2 \cdot 25}

x_{1, 2} = \frac{- 20 \sqrt{3} \pm \sqrt{1200 - 6100}}{50}

x_{1, 2} = \frac{- 20 \sqrt{3} \pm \sqrt{- 4900}}{50}

$x_{1, 2} = \frac{- 20 \sqrt{3} \pm \sqrt{4900} \cdot \sqrt{- 1}}{50}$

$x_{1, 2} = \frac{- 20 \sqrt{3} \pm 70 \cdot i}{50}$

$x_{1} = - \frac{2 \sqrt{3} + 70 i}{5}; x_{2} = - \frac{2 \sqrt{3} - 70 i}{5}$

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