1+3x-(3/4 x+5/4)^2=0

解

1 + 3 x - (\frac{3}{4} x + \frac{5}{4})^{2} = 0

x = 1

解答ステップ

1 + 3 x - (\frac{3}{4} x + \frac{5}{4})^{2} = 0

拡張

1 + 3 x - (\frac{3}{4} x + \frac{5}{4})^{2} : - \frac{9}{16} - \frac{9}{16} x^{2} + \frac{9}{8} x

- \frac{9}{16} - \frac{9}{16} x^{2} + \frac{9}{8} x = 0

標準的な形式で書く

a x^{2} + b x + c = 0

- \frac{9 x ^{2}}{16} + \frac{9 x}{8} - \frac{9}{16} = 0

解くとthe二次式

x_{1, 2} = \frac{- \frac{9}{8} \pm ( \frac{9}{8} ) ^{2} - 4 ( - \frac{9}{16} ) ( - \frac{9}{16} )}{2 ( - \frac{9}{16} )}

(\frac{9}{8})^{2} - 4 (- \frac{9}{16}) (- \frac{9}{16}) = 0

x_{1, 2} = \frac{- \frac{9}{8} \pm 0}{2 ( - \frac{9}{16} )}

x = \frac{- \frac{9}{8}}{2 ( - \frac{9}{16} )}

\frac{- \frac{9}{8}}{2 ( - \frac{9}{16} )} = 1

x = 1

二次equationの解:

x = 1