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受欢迎的代数 >

solvefor a,(16)^3=a^3a^2bb^2ab^3

解答

求解

a, (16)^{3} = a^{3} a^{2} b b^{2} a b^{3}

解答

a = \frac{4}{b}, a = - \frac{4}{b}

求解步骤

(16)^{3} = a^{3} a^{2} b b^{2} a b^{3}

交换两边

a^{3} a^{2} b b^{2} a b^{3} = 1 6^{3}

化简

a^{6} b^{6} = 4096

两边除以

b^{6}; b \neq = 0

\frac{a ^{6} b ^{6}}{b ^{6}} = \frac{4096}{b ^{6}}; b \neq = 0

a^{6} = \frac{4096}{b ^{6}}; b \neq = 0

用

u = a^{2}

和

u^{3} = a^{6}

改写方程式

u^{3} = \frac{4096}{b ^{6}}

解

u^{3} = \frac{4096}{b ^{6}} : u = 3 \frac{4096}{b ^{6}}, u = 3 \frac{4096}{b ^{6}} \frac{- 1 + 3 i}{2}, u = 3 \frac{4096}{b ^{6}} \frac{- 1 - 3 i}{2}

u = 3 \frac{4096}{b ^{6}}, u = 3 \frac{4096}{b ^{6}} \frac{- 1 + 3 i}{2}, u = 3 \frac{4096}{b ^{6}} \frac{- 1 - 3 i}{2}

代回

u = a^{2}

，求解

a

解

a^{2} = 3 \frac{4096}{b ^{6}} : a = \frac{4}{b}, a = - \frac{4}{b}

解

a^{2} = 3 \frac{4096}{b ^{6}} \frac{- 1 + 3 i}{2} :

无解

解

a^{2} = 3 \frac{4096}{b ^{6}} \frac{- 1 - 3 i}{2} :

无解

解为

a = \frac{4}{b}, a = - \frac{4}{b}

作图

流行的例子

d^2j^5x^4-22x^2+8=2

d^{2} j^{5} x^{4} - 22 x^{2} + 8 = 2

solvefor x,y-5=-2x(x^4)

so l v e f or x, y - 5 = - 2 x (x^{4})

x^{3} + 8000 = 0

(x^2-5)(x+3)-x^2=15

(x^{2} - 5) (x + 3) - x^{2} = 15

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