100t^2-192t+256=0

解

100 t^{2} - 192 t + 256 = 0

t = \frac{24}{25} + i \frac{32}{25}, t = \frac{24}{25} - i \frac{32}{25}

解答ステップ

100 t^{2} - 192 t + 256 = 0

解くとthe二次式

t_{1, 2} = \frac{- ( - 192 ) \pm ( - 192 ) ^{2} - 4 \cdot 100 \cdot 256}{2 \cdot 100}

簡素化

(- 192)^{2} - 4 \cdot 100 \cdot 256 : 256 i

t_{1, 2} = \frac{- ( - 192 ) \pm 256 i}{2 \cdot 100}

解を分離する

t_{1} = \frac{- ( - 192 ) + 256 i}{2 \cdot 100}, t_{2} = \frac{- ( - 192 ) - 256 i}{2 \cdot 100}

t = \frac{- ( - 192 ) + 256 i}{2 \cdot 100} : \frac{24}{25} + i \frac{32}{25}

t = \frac{- ( - 192 ) - 256 i}{2 \cdot 100} : \frac{24}{25} - i \frac{32}{25}

二次equationの解:

t = \frac{24}{25} + i \frac{32}{25}, t = \frac{24}{25} - i \frac{32}{25}