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受欢迎的代数 >

(((9-x)(3-sqrt(x))))/((3+sqrt(x)))=1

解答

\frac{( ( 9 - x ) ( 3 - x ) )}{( 3 + x )} = 1

解答

x = 4, x = 16

求解步骤

\frac{( ( 9 - x ) ( 3 - x ) )}{( 3 + x )} = 1

在两边乘以

3 + x

\frac{( 9 - x ) ( 3 - x )}{3 + x} (3 + x) = 1 \cdot (3 + x)

化简

(9 - x) (3 - x) = 3 + x

展开

(9 - x) (3 - x) : 27 - 9 x - 3 x + x x

27 - 9 x - 3 x + x x = 3 + x

因式分解

27 - 9 x - 3 x + x x : (x - 3) (x - 9)

(x - 3) (x - 9) = 3 + x

展开

(x - 3) (x - 9) : x x - 9 x - 3 x + 27

x x - 9 x - 3 x + 27 = 3 + x

将

3 x

到右边

x x - 9 x + 27 = 3 + x + 3 x

将

27

到右边

x x - 9 x = 3 x + x - 24

将

x

para o lado esquerdo

x x - 10 x = 3 x - 24

分解

x x - 10 x : x (x - 10)

x (x - 10) = 3 x - 24

两边除以

x - 10

x = \frac{3 x - 24}{x - 10}

两边进行平方:

x = \frac{9 x ^{2} - 144 x + 576}{x ^{2} - 20 x + 100}

x = \frac{9 x ^{2} - 144 x + 576}{x ^{2} - 20 x + 100}

解

x = \frac{9 x ^{2} - 144 x + 576}{x ^{2} - 20 x + 100} : x = 4, x = 9, x = 16

x = 4, x = 9, x = 16

验证解:

x = 4

真

, x = 9

假

, x = 16

真

解为

x = 4, x = 16

作图

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