r^2-12sqrt(3)r+80=0

解

r^{2} - 123 r + 80 = 0

r = 2 (33 + 7), r = 2 (33 - 7)

十進法表記

r = 15.68380 \dots, r = 5.10080 \dots

解答ステップ

r^{2} - 123 r + 80 = 0

解くとthe二次式

r_{1, 2} = \frac{- ( - 12 3 ) \pm ( - 12 3 ) ^{2} - 4 \cdot 1 \cdot 80}{2 \cdot 1}

(- 123)^{2} - 4 \cdot 1 \cdot 80 = 47

r_{1, 2} = \frac{- ( - 12 3 ) \pm 4 7}{2 \cdot 1}

解を分離する

r_{1} = \frac{- ( - 12 3 ) + 4 7}{2 \cdot 1}, r_{2} = \frac{- ( - 12 3 ) - 4 7}{2 \cdot 1}

r = \frac{- ( - 12 3 ) + 4 7}{2 \cdot 1} : 2 (33 + 7)

r = \frac{- ( - 12 3 ) - 4 7}{2 \cdot 1} : 2 (33 - 7)

二次equationの解:

r = 2 (33 + 7), r = 2 (33 - 7)