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受欢迎的代数 >

solvefor y,y^4=y^2-x^2

解答

求解

y, y^{4} = y^{2} - x^{2}

解答

y = \frac{1 + 1 - 4 x ^{2}}{2}, y = - \frac{1 + 1 - 4 x ^{2}}{2}, y = \frac{1 - 1 - 4 x ^{2}}{2}, y = - \frac{1 - 1 - 4 x ^{2}}{2}

求解步骤

y^{4} = y^{2} - x^{2}

将

x^{2}

para o lado esquerdo

y^{4} + x^{2} = y^{2}

将

y^{2}

para o lado esquerdo

y^{4} + x^{2} - y^{2} = 0

改写成标准形式

a_{n} x^{n} + \dots + a_{1} x + x = 0

y^{4} - y^{2} + x^{2} = 0

用

u = y^{2}

和

u^{2} = y^{4}

改写方程式

u^{2} - u + x^{2} = 0

解

u^{2} - u + x^{2} = 0 : u = \frac{1 + 1 - 4 x ^{2}}{2}, u = \frac{1 - 1 - 4 x ^{2}}{2}

u = \frac{1 + 1 - 4 x ^{2}}{2}, u = \frac{1 - 1 - 4 x ^{2}}{2}

代回

u = y^{2}

，求解

y

解

y^{2} = \frac{1 + 1 - 4 x ^{2}}{2} : y = \frac{1 + 1 - 4 x ^{2}}{2}, y = - \frac{1 + 1 - 4 x ^{2}}{2}

解

y^{2} = \frac{1 - 1 - 4 x ^{2}}{2} : y = \frac{1 - 1 - 4 x ^{2}}{2}, y = - \frac{1 - 1 - 4 x ^{2}}{2}

解为

y = \frac{1 + 1 - 4 x ^{2}}{2}, y = - \frac{1 + 1 - 4 x ^{2}}{2}, y = \frac{1 - 1 - 4 x ^{2}}{2}, y = - \frac{1 - 1 - 4 x ^{2}}{2}

作图

流行的例子

roo t s 2 x^{2} - 5 x - 6

2(x-2)^2-39=-31

2 (x - 2)^{2} - 39 = - 31

3 x^{2} - 14 x + 4 = 0

2 (x + 2)^{2} - 41 = - 9

3 x^{2} - 41 x + 26 = 0