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受欢迎的代数 >

1/x+6= 5/(sqrt(x))

解答

\frac{1}{x} + 6 = \frac{5}{x}

解答

x = \frac{1}{9}, x = \frac{1}{4}

+1

十进制

x = 0.11111 \dots, x = 0.25

求解步骤

\frac{1}{x} + 6 = \frac{5}{x}

找到

x, x

的最小公倍数:

x x

乘以最小公倍数=

x x

\frac{1}{x} x x + 6 x x = \frac{5}{x} x x

化简

x + 6 x x = 5 x

因式分解

x + 6 x x : x (6 x + 1)

x (6 x + 1) = 5 x

两边进行平方:

36 x^{3} + 12 x^{2} + x = 25 x^{2}

36 x^{3} + 12 x^{2} + x = 25 x^{2}

解

36 x^{3} + 12 x^{2} + x = 25 x^{2} : x = 0, x = \frac{1}{9}, x = \frac{1}{4}

x = 0, x = \frac{1}{9}, x = \frac{1}{4}

验证解:

x = 0

假

, x = \frac{1}{9}

真

, x = \frac{1}{4}

真

解为

x = \frac{1}{9}, x = \frac{1}{4}

作图

流行的例子

sqrt(x)-6=sqrt(x-3)

x - 6 = x - 3

sqrt(x-5)=sqrt(2x-6)-2

x - 5 = 2 x - 6 - 2

6x-5sqrt(x)-6=0

6 x - 5 x - 6 = 0

sqrt(x)-1=sqrt(x-9)

x - 1 = x - 9

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