x^2+(pi-1)x-pi=0

解

x^{2} + (π - 1) x - π = 0

x = \frac{- π + 1 + π ^{2} + 2 π + 1}{2}, x = \frac{- π + 1 - π ^{2} + 2 π + 1}{2}

十進法表記

x = 1, x = - 3.14159 \dots

解答ステップ

x^{2} + (π - 1) x - π = 0

解くとthe二次式

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

(π - 1)^{2} - 4 \cdot 1 \cdot (- π) = π^{2} + 2 π + 1

x_{1, 2} = \frac{- ( π - 1 ) \pm π ^{2} + 2 π + 1}{2 \cdot 1}

解を分離する

x_{1} = \frac{- ( π - 1 ) + π ^{2} + 2 π + 1}{2 \cdot 1}, x_{2} = \frac{- ( π - 1 ) - π ^{2} + 2 π + 1}{2 \cdot 1}

x = \frac{- ( π - 1 ) + π ^{2} + 2 π + 1}{2 \cdot 1} : \frac{- π + 1 + π ^{2} + 2 π + 1}{2}

x = \frac{- ( π - 1 ) - π ^{2} + 2 π + 1}{2 \cdot 1} : \frac{- π + 1 - π ^{2} + 2 π + 1}{2}

二次equationの解:

x = \frac{- π + 1 + π ^{2} + 2 π + 1}{2}, x = \frac{- π + 1 - π ^{2} + 2 π + 1}{2}