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受欢迎的代数 >

solvefor x,10x^9-9x^{10}=0.75

解答

求解

x, 10 x^{9} - 9 x^{10} = 0.75

解答

x \approx 1.06304 \dots, x \approx 0.90359 \dots

求解步骤

10 x^{9} - 9 x^{10} = 0.75

在两边乘以

100

1000 x^{9} - 900 x^{10} = 75

将

75

para o lado esquerdo

1000 x^{9} - 900 x^{10} - 75 = 0

改写成标准形式

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

- 900 x^{10} + 1000 x^{9} - 75 = 0

使用牛顿-拉弗森方法找到

- 900 x^{10} + 1000 x^{9} - 75 = 0

的一个解:

x \approx 1.06304 \dots

使用长除法

Eq u a t i o n 0 : \frac{- 900 x ^{10} + 1000 x ^{9} - 75}{x - 1.06304 \dots} = - 900 x^{9} + 43.26200 \dots x^{8} + 45.98933 \dots x^{7} + 48.88860 \dots x^{6} + 51.97065 \dots x^{5} + 55.24700 \dots x^{4} + 58.72989 \dots x^{3} + 62.43235 \dots x^{2} + 66.36823 \dots x + 70.55223 \dots

- 900 x^{9} + 43.26200 \dots x^{8} + 45.98933 \dots x^{7} + 48.88860 \dots x^{6} + 51.97065 \dots x^{5} + 55.24700 \dots x^{4} + 58.72989 \dots x^{3} + 62.43235 \dots x^{2} + 66.36823 \dots x + 70.55223 \dots \approx 0

使用牛顿-拉弗森方法找到

- 900 x^{9} + 43.26200 \dots x^{8} + 45.98933 \dots x^{7} + 48.88860 \dots x^{6} + 51.97065 \dots x^{5} + 55.24700 \dots x^{4} + 58.72989 \dots x^{3} + 62.43235 \dots x^{2} + 66.36823 \dots x + 70.55223 \dots = 0

的一个解:

x \approx 0.90359 \dots

使用长除法

Eq u a t i o n 0 : \frac{- 900 x ^{9} + 43.26200 \dots x ^{8} + 45.98933 \dots x ^{7} + 48.88860 \dots x ^{6} + 51.97065 \dots x ^{5} + 55.24700 \dots x ^{4} + 58.72989 \dots x ^{3} + 62.43235 \dots x ^{2} + 66.36823 \dots x + 70.55223 \dots}{x - 0.90359 \dots} = - 900 x^{8} - 769.97452 \dots x^{7} - 649.75667 \dots x^{6} - 538.22901 \dots x^{5} - 434.37101 \dots x^{4} - 337.24897 \dots x^{3} - 246.00697 \dots x^{2} - 159.85860 \dots x - 78.07938 \dots

- 900 x^{8} - 769.97452 \dots x^{7} - 649.75667 \dots x^{6} - 538.22901 \dots x^{5} - 434.37101 \dots x^{4} - 337.24897 \dots x^{3} - 246.00697 \dots x^{2} - 159.85860 \dots x - 78.07938 \dots \approx 0

使用牛顿-拉弗森方法找到

- 900 x^{8} - 769.97452 \dots x^{7} - 649.75667 \dots x^{6} - 538.22901 \dots x^{5} - 434.37101 \dots x^{4} - 337.24897 \dots x^{3} - 246.00697 \dots x^{2} - 159.85860 \dots x - 78.07938 \dots = 0

的一个解:

x \in R

无解

解为

x \approx 1.06304 \dots, x \approx 0.90359 \dots

作图

流行的例子

- x^{3} + 8 x = 0

-x^4+7x^2-3x-19=0

- x^{4} + 7 x^{2} - 3 x - 19 = 0

5x^3+45x^2+70x=0

5 x^{3} + 45 x^{2} + 70 x = 0

(x + 4)^{3} = 0

roo t s (x - 1)^{3}