zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的代数 >

solvefor x,csiny+x^2y=c

解答

求解

x, cs in y + x^{2} y = c

解答

x = \frac{c ( n ^{2} s ^{2} y ^{2} + 1 + 1 )}{2 y} - \frac{n c s y}{2 n ^{2} s ^{2} y ^{2} + 1 + 1} i, x = - \frac{c ( n ^{2} s ^{2} y ^{2} + 1 + 1 )}{2 y} + \frac{n c s y}{2 n ^{2} s ^{2} y ^{2} + 1 + 1} i, x = \frac{c ( - n ^{2} s ^{2} y ^{2} + 1 + 1 )}{2 y} - \frac{n c s y}{2 - n ^{2} s ^{2} y ^{2} + 1 + 1} i, x = - \frac{c ( - n ^{2} s ^{2} y ^{2} + 1 + 1 )}{2 y} + \frac{n c s y}{2 - n ^{2} s ^{2} y ^{2} + 1 + 1} i

求解步骤

cs in y + x^{2} y = c

替代

x = a + bi

cs in y + (a + bi)^{2} y = c

展开

cs in y + (a + bi)^{2} y : (y a^{2} - y b^{2}) + i (2 y ab + c n sy)

y a^{2} - y b^{2} + i (2 y ab + c n sy) = c

将

c

改写成标准复数形式:

c + 0 i

y a^{2} - y b^{2} + i (2 y ab + c n sy) = c + 0 i

复数仅在实部和虚部均相等时才相等改写为方程组:

[y a^{2} - y b^{2} = c 2 y ab + c n sy = 0]

[y a^{2} - y b^{2} = c 2 y ab + c n sy = 0] : a = \frac{c ( n ^{2} s ^{2} y ^{2} + 1 + 1 )}{2 y}, a = - \frac{c ( n ^{2} s ^{2} y ^{2} + 1 + 1 )}{2 y}, a = \frac{c ( - n ^{2} s ^{2} y ^{2} + 1 + 1 )}{2 y}, a = - \frac{c ( - n ^{2} s ^{2} y ^{2} + 1 + 1 )}{2 y}, b = - \frac{n c s y}{2 n ^{2} s ^{2} y ^{2} + 1 + 1} b = \frac{n c s y}{2 n ^{2} s ^{2} y ^{2} + 1 + 1} b = - \frac{n c s y}{2 - n ^{2} s ^{2} y ^{2} + 1 + 1} b = \frac{n c s y}{2 - n ^{2} s ^{2} y ^{2} + 1 + 1}

x = a + bi

代回

x = \frac{c ( n ^{2} s ^{2} y ^{2} + 1 + 1 )}{2 y} - \frac{n c s y}{2 n ^{2} s ^{2} y ^{2} + 1 + 1} i, x = - \frac{c ( n ^{2} s ^{2} y ^{2} + 1 + 1 )}{2 y} + \frac{n c s y}{2 n ^{2} s ^{2} y ^{2} + 1 + 1} i, x = \frac{c ( - n ^{2} s ^{2} y ^{2} + 1 + 1 )}{2 y} - \frac{n c s y}{2 - n ^{2} s ^{2} y ^{2} + 1 + 1} i, x = - \frac{c ( - n ^{2} s ^{2} y ^{2} + 1 + 1 )}{2 y} + \frac{n c s y}{2 - n ^{2} s ^{2} y ^{2} + 1 + 1} i

流行的例子

4z^2+(-13+18i)z-5-10i=0

4 z^{2} + (- 13 + 18 i) z - 5 - 10 i = 0

x^{2} + 4 - 3 i = 0

-3ai-(-1-i)b=3a-2

- 3 ai - (- 1 - i) b = 3 a - 2

i (x) = \frac{1}{x}

z^{2} + 2 z + 1 + i = 0