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受欢迎的代数 >

x(1-x)=2x-xsqrt(1-x)-x

解答

x (1 - x) = 2 x - x 1 - x - x

解答

x = 0, x = \frac{- 1 + 5}{2}

+1

十进制

x = 0, x = 0.61803 \dots

求解步骤

x (1 - x) = 2 x - x 1 - x - x

两边减去

2 x - x 1 - x - x

x (1 - x) - (2 x - x 1 - x - x) = 2 x - x 1 - x - x - (2 x - x 1 - x - x)

化简

- x^{2} + 1 - x x = 0

因式分解

- x^{2} + 1 - x x : x (- x + 1 - x)

x (- x + 1 - x) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

x = 0 or - x + 1 - x = 0

解

- x + 1 - x = 0 : x = \frac{- 1 + 5}{2}

x = 0, x = \frac{- 1 + 5}{2}

验证解:

x = 0

真

, x = \frac{- 1 + 5}{2}

真

解为

x = 0, x = \frac{- 1 + 5}{2}

作图

流行的例子

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3 = x^{2} + (- 1)^{2}

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