solvefor x,g(3-i)=x^2-6x

解

解く

x, g (3 - i) = x^{2} - 6 x

x = \frac{- g + 6 - \frac{9 + 3 g + 10 g ^{2} + 54 g + 81}{2}}{2 - \frac{9 + 81 + 10 g ^{2} + 54 g + 3 g}{2}} + - \frac{9 + 3 g + 10 g ^{2} + 54 g + 81}{2} i, x = - \frac{- g - 6 - \frac{9 + 3 g + 10 g ^{2} + 54 g + 81}{2}}{2 - \frac{9 + 81 + 10 g ^{2} + 54 g + 3 g}{2}} - - \frac{9 + 3 g + 10 g ^{2} + 54 g + 81}{2} i, x = \frac{- g + 6 - \frac{9 + 3 g - 10 g ^{2} + 54 g + 81}{2}}{2 - \frac{9 - 81 + 10 g ^{2} + 54 g + 3 g}{2}} + - \frac{9 + 3 g - 10 g ^{2} + 54 g + 81}{2} i, x = - \frac{- g - 6 - \frac{9 + 3 g - 10 g ^{2} + 54 g + 81}{2}}{2 - \frac{9 - 81 + 10 g ^{2} + 54 g + 3 g}{2}} - - \frac{9 + 3 g - 10 g ^{2} + 54 g + 81}{2} i

解答ステップ

g (3 - i) = x^{2} - 6 x

代用

x = a + bi

g (3 - i) = (a + bi)^{2} - 6 (a + bi)

拡張

3 g - i g = (a^{2} - b^{2} - 6 a) + i (- 6 b + 2 ab)

複素数は, その実数部と虚数部が等しい場合にのみ等しくなるequation系として書き換える:

[3 g = a^{2} - b^{2} - 6 a - g = - 6 b + 2 ab]

[3 g = a^{2} - b^{2} - 6 a - g = - 6 b + 2 ab] : a = \frac{- g + 6 - \frac{9 + 3 g + 10 g ^{2} + 54 g + 81}{2}}{2 - \frac{9 + 81 + 10 g ^{2} + 54 g + 3 g}{2}}, a = - \frac{- g - 6 - \frac{9 + 3 g + 10 g ^{2} + 54 g + 81}{2}}{2 - \frac{9 + 81 + 10 g ^{2} + 54 g + 3 g}{2}}, a = \frac{- g + 6 - \frac{9 + 3 g - 10 g ^{2} + 54 g + 81}{2}}{2 - \frac{9 - 81 + 10 g ^{2} + 54 g + 3 g}{2}}, a = - \frac{- g - 6 - \frac{9 + 3 g - 10 g ^{2} + 54 g + 81}{2}}{2 - \frac{9 - 81 + 10 g ^{2} + 54 g + 3 g}{2}}, b = - \frac{9 + 3 g + 10 g ^{2} + 54 g + 81}{2} b = - - \frac{9 + 3 g + 10 g ^{2} + 54 g + 81}{2} b = - \frac{9 + 3 g - 10 g ^{2} + 54 g + 81}{2} b = - - \frac{9 + 3 g - 10 g ^{2} + 54 g + 81}{2}

代用を戻す

x = a + bi

x = \frac{- g + 6 - \frac{9 + 3 g + 10 g ^{2} + 54 g + 81}{2}}{2 - \frac{9 + 81 + 10 g ^{2} + 54 g + 3 g}{2}} + - \frac{9 + 3 g + 10 g ^{2} + 54 g + 81}{2} i, x = - \frac{- g - 6 - \frac{9 + 3 g + 10 g ^{2} + 54 g + 81}{2}}{2 - \frac{9 + 81 + 10 g ^{2} + 54 g + 3 g}{2}} - - \frac{9 + 3 g + 10 g ^{2} + 54 g + 81}{2} i, x = \frac{- g + 6 - \frac{9 + 3 g - 10 g ^{2} + 54 g + 81}{2}}{2 - \frac{9 - 81 + 10 g ^{2} + 54 g + 3 g}{2}} + - \frac{9 + 3 g - 10 g ^{2} + 54 g + 81}{2} i, x = - \frac{- g - 6 - \frac{9 + 3 g - 10 g ^{2} + 54 g + 81}{2}}{2 - \frac{9 - 81 + 10 g ^{2} + 54 g + 3 g}{2}} - - \frac{9 + 3 g - 10 g ^{2} + 54 g + 81}{2} i