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受欢迎的代数 >

7(x^2+3)^2-x^2=0

解答

7 (x^{2} + 3)^{2} - x^{2} = 0

解答

x = \frac{1}{2 7} + \frac{83}{2 7} i, x = - \frac{1}{2 7} - \frac{83}{2 7} i, x = \frac{1}{2 7} - \frac{83}{2 7} i, x = - \frac{1}{2 7} + \frac{83}{2 7} i

求解步骤

7 (x^{2} + 3)^{2} - x^{2} = 0

展开

7 (x^{2} + 3)^{2} - x^{2} : 7 x^{4} + 41 x^{2} + 63

7 x^{4} + 41 x^{2} + 63 = 0

用

u = x^{2}

和

u^{2} = x^{4}

改写方程式

7 u^{2} + 41 u + 63 = 0

解

7 u^{2} + 41 u + 63 = 0 : u = - \frac{41}{14} + i \frac{83}{14}, u = - \frac{41}{14} - i \frac{83}{14}

u = - \frac{41}{14} + i \frac{83}{14}, u = - \frac{41}{14} - i \frac{83}{14}

代回

u = x^{2}

，求解

x

解

x^{2} = - \frac{41}{14} + i \frac{83}{14} : x = \frac{1}{2 7} + \frac{83}{2 7} i, x = - \frac{1}{2 7} - \frac{83}{2 7} i

解

x^{2} = - \frac{41}{14} - i \frac{83}{14} : x = \frac{1}{2 7} - \frac{83}{2 7} i, x = - \frac{1}{2 7} + \frac{83}{2 7} i

解为

x = \frac{1}{2 7} + \frac{83}{2 7} i, x = - \frac{1}{2 7} - \frac{83}{2 7} i, x = \frac{1}{2 7} - \frac{83}{2 7} i, x = - \frac{1}{2 7} + \frac{83}{2 7} i

作图

流行的例子

100t^3-50*10^3*t-375*10^3=0

100 t^{3} - 50 \cdot 1 0^{3} \cdot t - 375 \cdot 1 0^{3} = 0

d^{3} - d^{2} - d + 4 = 0

0.0004x^4=20x^2

0.0004 x^{4} = 20 x^{2}

x^{10} = 5

solvefor x,x^3-y^3-z^3=4

so l v e f or x, x^{3} - y^{3} - z^{3} = 4