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受欢迎的代数 >

xx+((2x)/(x+2))^2=5

解答

xx + (\frac{2 x}{x + 2})^{2} = 5

解答

x = - 1, x = 2, x = - \frac{5}{2} + i \frac{15}{2}, x = - \frac{5}{2} - i \frac{15}{2}

求解步骤

xx + (\frac{2 x}{x + 2})^{2} = 5

化简

(\frac{2 x}{x + 2})^{2} : \frac{4 x ^{2}}{( x + 2 ) ^{2}}

xx + \frac{4 x ^{2}}{( x + 2 ) ^{2}} = 5

在两边乘以

(x + 2)^{2}

x^{2} (x + 2)^{2} + 4 x^{2} = 5 (x + 2)^{2}

解

x^{2} (x + 2)^{2} + 4 x^{2} = 5 (x + 2)^{2} : x = - 1, x = 2, x = - \frac{5}{2} + i \frac{15}{2}, x = - \frac{5}{2} - i \frac{15}{2}

x = - 1, x = 2, x = - \frac{5}{2} + i \frac{15}{2}, x = - \frac{5}{2} - i \frac{15}{2}

验证解

找到无定义的点（奇点）:

x = - 2

将不在定义域的点与解相综合:

x = - 1, x = 2, x = - \frac{5}{2} + i \frac{15}{2}, x = - \frac{5}{2} - i \frac{15}{2}

作图

流行的例子

\frac{2}{2 x + 3} = \frac{1}{8}

x = \frac{4}{( \frac{2}{x} ) ^{2}}

2x-(16)/(x^2)=0

2 x - \frac{16}{x ^{2}} = 0

\frac{1}{2 x} = 6

\frac{1}{2 x} = 4