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受欢迎的代数 >

t^{-9}-9t^{-3}+8=0

解答

t^{- 9} - 9 t^{- 3} + 8 = 0

解答

t = 1, t = - \frac{1}{2} + \frac{3}{2} i, t = - \frac{1}{2} - \frac{3}{2} i, t = \frac{3 1 + 33}{2 3 2}, t = \frac{3 1 + 33 ( - \frac{1}{2} + \frac{3}{2} i )}{2 3 2}, t = \frac{3 1 + 33 ( - \frac{1}{2} - \frac{3}{2} i )}{2 3 2}, t = 3 \frac{1 - 33}{16}, t = - 3 \frac{1 - 33}{16} \frac{1}{2} + 3 \frac{1 - 33}{16} \frac{3}{2} i, t = - 3 \frac{1 - 33}{16} \frac{1}{2} - 3 \frac{1 - 33}{16} \frac{3}{2} i

求解步骤

t^{- 9} - 9 t^{- 3} + 8 = 0

整理后得

\frac{1}{t ^{9}} - \frac{9}{t ^{3}} + 8 = 0

乘以最小公倍数

1 - 9 t^{6} + 8 t^{9} = 0

解

1 - 9 t^{6} + 8 t^{9} = 0 : t = 1, t = - \frac{1}{2} + \frac{3}{2} i, t = - \frac{1}{2} - \frac{3}{2} i, t = \frac{3 1 + 33}{2 3 2}, t = \frac{3 1 + 33 ( - \frac{1}{2} + \frac{3}{2} i )}{2 3 2}, t = \frac{3 1 + 33 ( - \frac{1}{2} - \frac{3}{2} i )}{2 3 2}, t = 3 \frac{1 - 33}{16}, t = - 3 \frac{1 - 33}{16} \frac{1}{2} + 3 \frac{1 - 33}{16} \frac{3}{2} i, t = - 3 \frac{1 - 33}{16} \frac{1}{2} - 3 \frac{1 - 33}{16} \frac{3}{2} i

t = 1, t = - \frac{1}{2} + \frac{3}{2} i, t = - \frac{1}{2} - \frac{3}{2} i, t = \frac{3 1 + 33}{2 3 2}, t = \frac{3 1 + 33 ( - \frac{1}{2} + \frac{3}{2} i )}{2 3 2}, t = \frac{3 1 + 33 ( - \frac{1}{2} - \frac{3}{2} i )}{2 3 2}, t = 3 \frac{1 - 33}{16}, t = - 3 \frac{1 - 33}{16} \frac{1}{2} + 3 \frac{1 - 33}{16} \frac{3}{2} i, t = - 3 \frac{1 - 33}{16} \frac{1}{2} - 3 \frac{1 - 33}{16} \frac{3}{2} i

验证解

找到无定义的点（奇点）:

t = 0

将不在定义域的点与解相综合:

t = 1, t = - \frac{1}{2} + \frac{3}{2} i, t = - \frac{1}{2} - \frac{3}{2} i, t = \frac{3 1 + 33}{2 3 2}, t = \frac{3 1 + 33 ( - \frac{1}{2} + \frac{3}{2} i )}{2 3 2}, t = \frac{3 1 + 33 ( - \frac{1}{2} - \frac{3}{2} i )}{2 3 2}, t = 3 \frac{1 - 33}{16}, t = - 3 \frac{1 - 33}{16} \frac{1}{2} + 3 \frac{1 - 33}{16} \frac{3}{2} i, t = - 3 \frac{1 - 33}{16} \frac{1}{2} - 3 \frac{1 - 33}{16} \frac{3}{2} i

作图

流行的例子

6-1/(x+1)= 6/(x+2)

6 - \frac{1}{x + 1} = \frac{6}{x + 2}

x + 2 + \frac{1}{x} = 0

1/x =(3.55)/(1.22)

\frac{1}{x} = \frac{3.55}{1.22}

solvefor p,(1-p)/p =x

so l v e f or p, \frac{1 - p}{p} = x

\frac{1}{t + 1} - 0.1 = 0