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受欢迎的代数 >

2u^{2/3}+7u^{1/3}=4

解答

2 u^{\frac{2}{3}} + 7 u^{\frac{1}{3}} = 4

解答

u = \frac{1}{8}, u = - 64

+1

十进制

u = 0.125, u = - 64

求解步骤

2 u^{\frac{2}{3}} + 7 u^{\frac{1}{3}} = 4

使用以下的指数特性

: a^{\frac{n}{m}} = (a^{\frac{1}{m}})^{n}

u^{\frac{2}{3}} = (u^{\frac{1}{3}})^{2}

2 (u^{\frac{1}{3}})^{2} + 7 u^{\frac{1}{3}} = 4

用

u^{\frac{1}{3}} = v

改写方程式

2 v^{2} + 7 v = 4

解

2 v^{2} + 7 v = 4 : v = \frac{1}{2}, v = - 4

v = \frac{1}{2}, v = - 4

代回

v = u^{\frac{1}{3}}

，求解

u

解

u^{\frac{1}{3}} = \frac{1}{2} : u = \frac{1}{8}

解

u^{\frac{1}{3}} = - 4 : u = - 64

u = \frac{1}{8}, u = - 64

验证解:

u = \frac{1}{8}

真

, u = - 64

真

解为

u = \frac{1}{8}, u = - 64

作图

流行的例子

x + 2 = 2 x + 7

1= 1/(3x^{2/3)}

1 = \frac{1}{3 x ^{\frac{2}{3}}}

(37-2x^2)/(sqrt(37-x^2))=0

\frac{37 - 2 x ^{2}}{37 - x ^{2}} = 0

2sqrt(x)= 2/3 x^2-16/3 x

2 x = \frac{2}{3} x^{2} - \frac{16}{3} x

solvefor x,16x-40x^{1/2}+9=0

so l v e f or x, 16 x - 40 x^{\frac{1}{2}} + 9 = 0