solvefor x,4x^2-kx+4=0

解

x, 4 x^{2} - k x + 4 = 0

x = \frac{k + k ^{2} - 64}{8}, x = \frac{k - k ^{2} - 64}{8}

解答ステップ

4 x^{2} - k x + 4 = 0

解くとthe二次式

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

簡素化

(- k)^{2} - 4 \cdot 4 \cdot 4 : k^{2} - 64

x_{1, 2} = \frac{- ( - k ) \pm k ^{2} - 64}{2 \cdot 4}

解を分離する

x_{1} = \frac{- ( - k ) + k ^{2} - 64}{2 \cdot 4}, x_{2} = \frac{- ( - k ) - k ^{2} - 64}{2 \cdot 4}

x = \frac{- ( - k ) + k ^{2} - 64}{2 \cdot 4} : \frac{k + k ^{2} - 64}{8}

x = \frac{- ( - k ) - k ^{2} - 64}{2 \cdot 4} : \frac{k - k ^{2} - 64}{8}

二次equationの解:

x = \frac{k + k ^{2} - 64}{8}, x = \frac{k - k ^{2} - 64}{8}