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受欢迎的代数 >

x=2+sqrt(3)sqrt(x)+1sqrt(x)

解答

x = 2 + 3 x + 1 x

解答

x = 2 9 - 43 + 3 9 - 43 + 4 + 3

+1

十进制

x = 11.10386 \dots

求解步骤

x = 2 + 3 x + 1 \cdot x

展开

2 + 3 x + 1 \cdot x : 2 + 3 x + x

x = 2 + 3 x + x

交换两边

2 + 3 x + x = x

将

2

到右边

3 x + x = x - 2

分解

3 x + x : (3 + 1) x

(3 + 1) x = x - 2

两边除以

3 + 1

x = \frac{( 3 - 1 ) ( x - 2 )}{2}

两边进行平方:

x = x^{2} - \frac{3 x ^{2}}{2} + 23 x - 4 x + 4 - 23

x = x^{2} - \frac{3 x ^{2}}{2} + 23 x - 4 x + 4 - 23

解

x = x^{2} - \frac{3 x ^{2}}{2} + 23 x - 4 x + 4 - 23 : x = 2 9 - 43 + 3 9 - 43 + 4 + 3, x = - 2 9 - 43 - 3 9 - 43 + 4 + 3

x = 2 9 - 43 + 3 9 - 43 + 4 + 3, x = - 2 9 - 43 - 3 9 - 43 + 4 + 3

验证解:

x = 2 9 - 43 + 3 9 - 43 + 4 + 3

真

, x = - 2 9 - 43 - 3 9 - 43 + 4 + 3

假

解是

x = 2 9 - 43 + 3 9 - 43 + 4 + 3

作图

流行的例子

x^{\frac{3}{2}} = 12

sqrt(4-3x)-2sqrt(36-27x)+5=0

4 - 3 x - 2 36 - 27 x + 5 = 0

(-1)/(5-sqrt(1/3*x+1))=-17/10

\frac{- 1}{5 - \frac{1}{3} \cdot x + 1} = - \frac{17}{10}

solvefor x,20g*sqrt(x^3-9^2)=2

so l v e f or x, 20 g \cdot x^{3} - 9^{2} = 2

x-2=sqrt(-2x+14)

x - 2 = - 2 x + 14