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受欢迎的代数 >

23=x^2+(1/(x^2))

解答

23 = x^{2} + (\frac{1}{x ^{2}})

解答

x = \frac{23 + 5 21}{2}, x = - \frac{23 + 5 21}{2}, x = \frac{23 - 5 21}{2}, x = - \frac{23 - 5 21}{2}

+1

十进制

x = 4.79128 \dots, x = - 4.79128 \dots, x = 0.20871 \dots, x = - 0.20871 \dots

求解步骤

23 = x^{2} + (\frac{1}{x ^{2}})

化简

(\frac{1}{x ^{2}}) : \frac{1}{x ^{2}}

23 = x^{2} + \frac{1}{x ^{2}}

在两边乘以

x^{2}

23 x^{2} = x^{4} + 1

解

23 x^{2} = x^{4} + 1 : x = \frac{23 + 5 21}{2}, x = - \frac{23 + 5 21}{2}, x = \frac{23 - 5 21}{2}, x = - \frac{23 - 5 21}{2}

x = \frac{23 + 5 21}{2}, x = - \frac{23 + 5 21}{2}, x = \frac{23 - 5 21}{2}, x = - \frac{23 - 5 21}{2}

验证解

找到无定义的点（奇点）:

x = 0

将不在定义域的点与解相综合:

x = \frac{23 + 5 21}{2}, x = - \frac{23 + 5 21}{2}, x = \frac{23 - 5 21}{2}, x = - \frac{23 - 5 21}{2}

作图

流行的例子

x/(x-2)+3/(x+4)=2

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

1-x/(x+2)= x/(x-3)

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

2 - \frac{1}{x} = 1.1

x/(x-2)=((2x-3))/x

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

\frac{10}{3} = \frac{4}{x} + 2