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受欢迎的代数 >

sqrt(x^2+6x)=x+sqrt(2x)

解答

x^{2} + 6 x = x + 2 x

解答

x = 0, x = 2

求解步骤

x^{2} + 6 x = x + 2 x

两边进行平方:

x^{2} + 6 x = x^{2} + 2 2 x x + 2 x

x^{2} + 6 x = x^{2} + 2 2 x x + 2 x

两边减去

x^{2} + 2 2 x x + 2 x

x^{2} + 6 x - (x^{2} + 2 2 x x + 2 x) = x^{2} + 2 2 x x + 2 x - (x^{2} + 2 2 x x + 2 x)

化简

- 2 2 x x + 4 x = 0

因式分解

- 2 2 x x + 4 x : - 2 x (2 x - 2)

- 2 x (2 x - 2) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

x = 0 or 2 x - 2 = 0

解

2 x - 2 = 0 : x = 2

x = 0, x = 2

验证解:

x = 0

真

, x = 2

真

解为

x = 0, x = 2

作图

流行的例子

sqrt(2v)=sqrt(3v-1)

2 v = 3 v - 1

x + 1 = 2

3 = \frac{x}{5}

6x+11sqrt(x)-35=0

6 x + 11 x - 35 = 0

sqrt(3x)+11=x+5

3 x + 11 = x + 5