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受欢迎的代数 >

(72)/((x^{8/5))}=((x^{7/5}))/(24)

解答

\frac{72}{( x ^{\frac{8}{5}} )} = \frac{( x ^{\frac{7}{5}} )}{24}

解答

x = 12

求解步骤

\frac{72}{( x ^{\frac{8}{5}} )} = \frac{( x ^{\frac{7}{5}} )}{24}

使用分式交叉相乘: 若

\frac{a}{b} = \frac{c}{d}

则

a \cdot d = b \cdot c

72 \cdot 24 = x^{\frac{8}{5}} x^{\frac{7}{5}}

将

x^{\frac{8}{5}} x^{\frac{7}{5}}

para o lado esquerdo

1728 - x^{\frac{8}{5}} x^{\frac{7}{5}} = 0

因式分解

1728 - x^{\frac{8}{5}} x^{\frac{7}{5}} : - (x - 12) (x^{2} + 12 x + 144)

- (x - 12) (x^{2} + 12 x + 144) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

x - 12 = 0 or x^{2} + 12 x + 144 = 0

解

x - 12 = 0 : x = 12

解

x^{2} + 12 x + 144 = 0 : x \in R

无解

x = 12

验证解:

x = 12

真

解是

x = 12

作图

流行的例子

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

x^{2} - x = 3 - x

sqrt(x+2\sqrt{x-1)}=2

x + 2 x - 1 = 2

2x^2-2sqrt(6x)+3=0

2 x^{2} - 2 6 x + 3 = 0

x - 3 = 5 - x

x^{(-3)/4}= 1/8

x^{\frac{- 3}{4}} = \frac{1}{8}