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受欢迎的代数 >

solvefor x,y^2=2x^4+6

解答

求解

x, y^{2} = 2 x^{4} + 6

解答

x = \frac{y ^{2} - 6}{2}, x = - \frac{y ^{2} - 6}{2}, x = i 4 \frac{y ^{2} - 6}{2}, x = - i 4 \frac{y ^{2} - 6}{2}

求解步骤

y^{2} = 2 x^{4} + 6

交换两边

2 x^{4} + 6 = y^{2}

将

6

到右边

2 x^{4} = y^{2} - 6

两边除以

2

x^{4} = \frac{y ^{2} - 6}{2}

用

u = x^{2}

和

u^{2} = x^{4}

改写方程式

u^{2} = \frac{y ^{2} - 6}{2}

解

u^{2} = \frac{y ^{2} - 6}{2} : u = \frac{y ^{2} - 6}{2}, u = - \frac{y ^{2} - 6}{2}

u = \frac{y ^{2} - 6}{2}, u = - \frac{y ^{2} - 6}{2}

代回

u = x^{2}

，求解

x

解

x^{2} = \frac{y ^{2} - 6}{2} : x = \frac{y ^{2} - 6}{2}, x = - \frac{y ^{2} - 6}{2}

解

x^{2} = - \frac{y ^{2} - 6}{2} : x = i 4 \frac{y ^{2} - 6}{2}, x = - i 4 \frac{y ^{2} - 6}{2}

解为

x = \frac{y ^{2} - 6}{2}, x = - \frac{y ^{2} - 6}{2}, x = i 4 \frac{y ^{2} - 6}{2}, x = - i 4 \frac{y ^{2} - 6}{2}

作图

流行的例子

x^{5} = 64

3 x^{2} = 9 x^{3}

(x+2)^4=(x-10)^2

(x + 2)^{4} = (x - 10)^{2}

x^{5} = - 2

solvefor x,3y^3=3x^3+11y-3

so l v e f or x, 3 y^{3} = 3 x^{3} + 11 y - 3