3q^2-120q+1000=0

解

3 q^{2} - 120 q + 1000 = 0

q = \frac{10 ( 6 + 6 )}{3}, q = \frac{10 ( 6 - 6 )}{3}

十進法表記

q = 28.16496 \dots, q = 11.83503 \dots

解答ステップ

3 q^{2} - 120 q + 1000 = 0

解くとthe二次式

q_{1, 2} = \frac{- ( - 120 ) \pm ( - 120 ) ^{2} - 4 \cdot 3 \cdot 1000}{2 \cdot 3}

(- 120)^{2} - 4 \cdot 3 \cdot 1000 = 206

q_{1, 2} = \frac{- ( - 120 ) \pm 20 6}{2 \cdot 3}

解を分離する

q_{1} = \frac{- ( - 120 ) + 20 6}{2 \cdot 3}, q_{2} = \frac{- ( - 120 ) - 20 6}{2 \cdot 3}

q = \frac{- ( - 120 ) + 20 6}{2 \cdot 3} : \frac{10 ( 6 + 6 )}{3}

q = \frac{- ( - 120 ) - 20 6}{2 \cdot 3} : \frac{10 ( 6 - 6 )}{3}

二次equationの解:

q = \frac{10 ( 6 + 6 )}{3}, q = \frac{10 ( 6 - 6 )}{3}