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受欢迎的代数 >

(-1)/(5-sqrt(1/5*x+1))= 17/10

解答

\frac{- 1}{5 - \frac{1}{5} \cdot x + 1} = \frac{17}{10}

解答

x = \frac{43680}{289}

+1

十进制

x = 151.14186 \dots

求解步骤

\frac{- 1}{5 - \frac{1}{5} x + 1} = \frac{17}{10}

使用分式交叉相乘: 若

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

则

a \cdot d = b \cdot c

(- 1) \cdot 10 = (5 - \frac{1}{5} x + 1) \cdot 17

展开

(5 - \frac{1}{5} x + 1) \cdot 17 : 85 - 17 \frac{1}{5} x + 1

(- 1) \cdot 10 = 85 - 17 \frac{1}{5} x + 1

交换两边

85 - 17 \frac{1}{5} x + 1 = (- 1) \cdot 10

去除括号:

(- a) = - a

85 - 17 \frac{1}{5} x + 1 = - 1 \cdot 10

数字相乘:

1 \cdot 10 = 10

85 - 17 \frac{1}{5} x + 1 = - 10

将

85

到右边

- 17 \frac{1}{5} x + 1 = - 95

两边除以

- 17

\frac{1}{5} x + 1 = \frac{95}{17}

两边进行平方:

\frac{1}{5} x + 1 = \frac{9025}{289}

\frac{1}{5} x + 1 = \frac{9025}{289}

解

\frac{1}{5} x + 1 = \frac{9025}{289} : x = \frac{43680}{289}

x = \frac{43680}{289}

验证解:

x = \frac{43680}{289}

真

解是

x = \frac{43680}{289}

作图

流行的例子

x + 9 - 5 = 4

x - 1 = 2

x - 1 = 8

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

x + x - x = 1

sqrt(x/((1-x)))+sqrt(((1-x))/x)= 21/6

\frac{x}{( 1 - x )} + \frac{( 1 - x )}{x} = \frac{21}{6}