solvefor x,y=-x^2+1graficar

解

解く

x, y = - x^{2} + 1 g r a f i c a r

x = - \frac{y + a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2} + \frac{a ^{2} c r ^{2} f g}{2 - \frac{y + a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2}} i, x = - - \frac{y + a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2} - \frac{a ^{2} c r ^{2} f g}{2 - \frac{y + a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2}} i, x = - \frac{y - a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2} + \frac{a ^{2} c r ^{2} f g}{2 - \frac{y - a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2}} i, x = - - \frac{y - a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2} - \frac{a ^{2} c r ^{2} f g}{2 - \frac{y - a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2}} i

解答ステップ

y = - x^{2} + 1 \cdot g r a f i c a r

代用

x = u + v i

y = - (u + v i)^{2} + 1 \cdot g r a f i c a r

拡張

- (u + v i)^{2} + 1 \cdot g r a f i c a r : (- u^{2} + v^{2}) + i (- 2 uv + a^{2} c r^{2} f g)

y = (- u^{2} + v^{2}) + i (- 2 uv + a^{2} c r^{2} f g)

標準的な複素数形式で

y

を書き換える:

y + 0 i

y + 0 i = (- u^{2} + v^{2}) + i (- 2 uv + a^{2} c r^{2} f g)

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:

[y = - u^{2} + v^{2} 0 = - 2 uv + a^{2} c r^{2} f g]

[y = - u^{2} + v^{2} 0 = - 2 uv + a^{2} c r^{2} f g] : u = - \frac{y + a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2}, u = - - \frac{y + a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2}, u = - \frac{y - a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2}, u = - - \frac{y - a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2}, v = \frac{a ^{2} c r ^{2} f g}{2 - \frac{y + a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2}} v = - \frac{a ^{2} c r ^{2} f g}{2 - \frac{y + a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2}} v = \frac{a ^{2} c r ^{2} f g}{2 - \frac{y - a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2}} v = - \frac{a ^{2} c r ^{2} f g}{2 - \frac{y - a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2}}

代用を戻す

x = u + v i

x = - \frac{y + a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2} + \frac{a ^{2} c r ^{2} f g}{2 - \frac{y + a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2}} i, x = - - \frac{y + a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2} - \frac{a ^{2} c r ^{2} f g}{2 - \frac{y + a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2}} i, x = - \frac{y - a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2} + \frac{a ^{2} c r ^{2} f g}{2 - \frac{y - a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2}} i, x = - - \frac{y - a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2} - \frac{a ^{2} c r ^{2} f g}{2 - \frac{y - a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2}} i