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受欢迎的代数 >

xsqrt(c^2x^2-1)=cx^2-x

解答

x c^{2} x^{2} - 1 = c x^{2} - x

解答

x = 0 {无解}, x = \frac{1}{c} {c < 0 or c > 0}

求解步骤

x c^{2} x^{2} - 1 = c x^{2} - x

两边减去

c x^{2} - x

x c^{2} x^{2} - 1 - (c x^{2} - x) = c x^{2} - x - (c x^{2} - x)

化简

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

因式分解

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

x (c^{2} x^{2} - 1 - c x + 1) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

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

解

c^{2} x^{2} - 1 - c x + 1 = 0 : x = \frac{1}{c} {c < 0 or c > 0}

x = 0, x = \frac{1}{c} {c < 0 or c > 0}

验证解:

x = 0 {无解}, x = \frac{1}{c} {c < 0 or c > 0}

解为

x = 0 {无解}, x = \frac{1}{c} {c < 0 or c > 0}

作图

流行的例子

x-6sqrt(x)-27=0

x - 6 x - 27 = 0

5 - 2 x - 3 = 0

\sqrt[3]{x+3}=5

3 x + 3 = 5

solvefor x,sqrt(3x)+x=0

so l v e f or x, 3 x + x = 0

y 3 y = 2